When the inequality sign is </> (less than/greater than), the dot is an open circle.
When the inequality sign is ≤/≥ (less than or equal to/greater than or equal to), the dot is a closed circle.
y = number that is a solution/makes the inequality true
y ≤ 8 (y is any number less than or equal to 8)
#1: y = 0 is part of the solution set.
Yes because if you substitute/plug in 0 into "y" in the inequality, since y = 0:
0 ≤ 8 0 is less than 8.
#2: y = 8 is part of the solution set.
Yes because if you plug it into the inequality:
8 ≤ 8 8 is equal to 8
#3: y = 10 is part of the solution set.
No because if you plug it into the inequality:
10 ≤ 8 10 is not less than or equal to 8
#4: There is an open circle on the graph at 8.
No because the inequality sign is ≤, so there should be a closed circle on 8.
#5: There is a closed circle on the graph at 8.
Yes because the inequality sign is ≤
#6: The arrow on the graph points left.
Yes because if the arrow is pointing left then the numbers are decreasing, and y is any number less than or equal to 8.
#7: The arrow on the graph points right.
No because if the arrow is point right then the numbers are increasing, but y is not a number greater than 8.
Your answer is the 1st, 2nd, 5th, and 6th option
To solve the problem first we need to understand the Inequality Signs.
Inequality SignIn an inequality sign there is a dot(circle) present, but whether the circle is open or closed depends, upon the inequality sign.
If the inequality sign is less than(<) or greater than(>), the dot is an open circle.
whereas, if the inequality sign is less than or equal to (≤) and greater than or equal to(≥), the dot is a closed circle.
The correct options are A, B, E, and F.
ExplanationGiven statements to us,
A.) y = 0 is part of the solution set.
B.) y = 8 is part of the solution set.
C.) y = 10 is part of the solution set.
D.) There is an open circle on the graph at 8.
E.) There is a closed circle on the graph at 8.
F.) The arrow on the graph points left.
G.) The arrow on the graph points right.
Solutions
We know that the number line is always decreasing number or negative towards the left while positive towards the right.
Therefore, y≤8 means, y is true for any value less than and equal to 8, which will give a closed circle on the graph, and the arrow will be pointing toward the left.
Now looking at the options we have,
A.) y = 0 is part of the solution set.
The statement is true as the y value is less than 8.
B.) y = 8 is part of the solution set.
The statement is true as the y value is equal to 8.
C.) y = 10 is part of the solution set.
The statement is false as the y value is greater than 8.
D.) There is an open circle on the graph at 8.
The statement is false as the inequality sign given is less than or equal to (≤).
E.) There is a closed circle on the graph at 8.
The statement is true as the inequality sign given is less than or equal to (≤).
F.) The arrow on the graph points left.
The statement is true as the value of y is always on the decreasing side, the number line is always decreasing the number or negative towards the left while positive towards the right.
G.) The arrow on the graph points right.
The statement is false as the value of y is always on the decreasing side, the number line is always decreasing the number or negative towards the left while positive towards the right.
Hence, the correct options are A, B, E, and F.
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can 45/5 be simplified
45/5 Simplified
What is 45/5 Simplified? - 9/1 is the simplified fraction for 45/5. Simplify 45/5 to the simplest form. Online simplify fractions calculator to reduce 45/5 to the lowest terms quickly and easily.
Simplify 45/5
Fraction:
45
------
5
45/5 Simplified
Answer:
45/5 = 9/1 = 9
Simplify 45/5
Simplify 45/5 reduces the fraction 45/5 to the lowest form. You can change the numerator or denominator to simplify any other fraction.
Use the diagram below to answer the following questions.
Name all segments parallel to XT.
Name all segments parallel to ZY.
Name all segments parallel to ZS.
Name a plane parallel to plane STU.
Name a plane parallel to plane UVZ.
Name all segments skew to SW.
Name all segments skew to UT.
HELPPPPPP PLEASE
Answer:
Segments parallel to XT: YU, ZV, WS
Segments parallel to ZY: VU, WX
Segments parallel to ZS: None
Plane parallel to plane STU: WXY
Plane parallel to plane UVZ: TSW
All segments skew to SW: WX, ST
All segments skew to UT: UY, TX
Step-by-step explanation:
Let's begin by explaining the following:
Two line segments are parallel only if their slopes are identical, allowing them to never intersect.
Hence, according to this definition we have:
Segments parallel to XT: YU, ZV, WS
Segments parallel to ZY: VU, WX
Segments parallel to ZS: None
Now, if we go to the three-dimensional space, two planes are parallel, when they do not share any line, which allows them to never cross in space.
Hence, according to this definition we have:
Plane parallel to plane STU: WXY
Plane parallel to plane UVZ: TSW
Two lines are skew if and only if they are not in the same plane (also known as not coplanar). So, if two lines are not coplanar, they are not parallel and cannot intersect, either.
Hence, according to this definition we have:
All segments skew to SW: WX, ST
WZ and SV do not match the condition, since they are in the same plane where SW is,
All segments skew to UT: UY, TX
UV and ST do not match the condition, since they are in the same plane where UT is.
The following answers can be given as the solution to the given questions:
a) All segments parallel to XT: YU, ZV, WS
b) All segments parallel to ZY: VU, WX
c) All segments parallel to ZS: YT
d) A plane parallel to plane STU: WXY
e) A plane parallel to plane UVZ: TSW
f) All segments skew to SW: ZY, VU, XY, UT
g) All segments skew to UT: SW, WX, VZ, ZY
To give the appropriate answers to the given questions, the following terms must be understood.
i. Parallel lines: Two or more lines are parallel if and only if they do not meet even when extended to infinity.
ii. Skew lines: Two or more skew lines are lines that are neither parallel nor intersecting.
iii. Plane: This is flat surface which can either be in x-axis, y-axis or z-axis.
Therefore, the answers to each of the questions are:
a) All segments parallel to XT: YU, ZV, WS
b) All segments parallel to ZY: VU, WX
c) All segments parallel to ZS: YT
d) A plane parallel to plane STU: WXY
e) A plane parallel to plane UVZ: TSW
f) All segments skew to SW: ZY, VU, XY, UT
g) All segments skew to UT: SW, WX, VZ, ZY
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1. Points A and B are in the first quadrant in the coordinate plane. What might be their coordinates?
2. Points D and E are in the second quadrant in the coordinate plane. What might be their coordinates?
3. Points G and H are in the third quadrant in the coordinate plane. What might be their coordinates?
4, Points J and K are in the fourth quadrant in the coordinate plane. What might be their coordinates?
5. Points M and N are on the y-axis in the coordinate plane. What might be their coordinates?
6. Points Q and Rare on the x-axis in the coordinate plane. What might be their coordinates?
Quadrant one: positive x and positive y. (5,6)
Quadrant two: negative x and positive y. (-5,6)
Quadrant three: negative x and negative y. (-5,-6)
Quadrant four: positive x and negative y. (5,-6)
the y-axis goes up and down so im guessing the x coordinates will be 0 and the y will be whatever you want it to be. the same goes for the x-axis excepted switched around.
Apologies if I got any of these wrong, and please comment if you are confused so I can explain more.
1.) First quadrant: x > 0, y > 0.
2.) Second quadrant: x < 0, y > 0.
3.) Third quadrant: x < 0, y < 0.
4.) Fourth quadrant: x > 0, y < 0.
5.) On y-axis: x = 0, y ≠ 0.
6.) On x-axis: x ≠ 0, y = 0.
1.) Points in the First Quadrant: In the first quadrant, both x and y coordinates are positive. Therefore, the coordinates of points A and B might be of the form (x, y) where x > 0 and y > 0. For instance, point A might be (3, 4) and point B might be (5, 7).
2.) Points in the Second Quadrant: In the second quadrant, x coordinates are negative and y coordinates are positive. Thus, the coordinates of points D and E might be of the form (-x, y) where x > 0 and y > 0. For example, point D might be (-2, 3) and point E might be (-6, 8).
3.) Points in the Third Quadrant: In the third quadrant, both x and y coordinates are negative. Therefore, the coordinates of points G and H might be of the form (-x, -y) where x > 0 and y > 0. For instance, point G might be (-4, -5) and point H might be (-7, -9).
4.) Points in the Fourth Quadrant: In the fourth quadrant, x coordinates are positive and y coordinates are negative. Thus, the coordinates of points J and K might be of the form (x, -y) where x > 0 and y > 0. For example, point J might be (3, -2) and point K might be (8, -5).
5.) Points on the Y-Axis: Points on the y-axis have x coordinates equal to 0, and their y coordinates can be positive or negative. Thus, the coordinates of points M and N might be of the form (0, y). For instance, point M might be (0, 4) and point N might be (0, -7).
6.) Points on the X-Axis: Points on the x-axis have y coordinates equal to 0, and their x coordinates can be positive or negative. Thus, the coordinates of points Q and R might be of the form (x, 0). For example, point Q might be (5, 0) and point R might be (-3, 0).
PLEASE ANSWER ASAP!!!
WHAT SHOULD 2.33 BE MULTIPLIED BY TO MAKE IT INTO A WHOLE NUMBRR??
Answer:
2.331 = (2.33 × 100)(1 × 100) = 233100. As the numerator is greater than the denominator, we have an IMPROPER fraction, so we can also express it as a MIXED NUMBER, thus 233100 is also equal to 233100 when expressed as a mixed number.
Step-by-step explanation:
or mutilpy by 100
Answer:
2.33 * 100 because
2.33*100=233
3. Use an inequality symbol (<, >, 2, =) to compare -26_54
OOOO
O A.<
O B. =
O c.
O D.>
It would be A or < since 54 is positive and -26 isn't, that makes 54 greater than -26.
An internet company, K-mobile, charges $60 per month for use of up to 100 hours but then charges $100 per month for 100 hours and more. Another company, AK & K, charges $1.50 per hour of use. When is the K-mobile a better deal?
What is the product of 2x-1 and 2x+6? Write your answer in standard form.
Show your work.
Is the product of 2x-1 and 2x+6 equal to the product of 1x-2 and 6+2x? Explain your answer.
Answers and Step-by-step explanations:
We need to use FOIL (first, outer, inner, last) to solve this.
The first terms of each of the two expressions (2x - 1) and (2x + 6) are 2x and 2x. Multiply these together: 2x * 2x = 4x².
The outer terms are 2x and 6, respectively, and their product is 2x * 6 = 12x.
The inner terms are -1 and 2x, respectively, and their product is -1 * 2x = -2x.
The last terms are -1 and 6, respectively, and their product is -1 * 6 = -6.
Add these together:
4x² + 12x + (-2x) + (-6) = 4x² + 10x - 6
Let's see if this is equal to (1x - 2) * (6 + 2x) by expanding this one using FOIL as well:
The first terms are 1x and 6, respectively, and their product is 1x * 6 = 6x.
The outer terms are 1x and 2x, respectively, and their product is 1x * 2x = 2x².
The inner terms are -2 and 6, respectively, and their product is -2 * 6 = -12.
The last terms are -2 and 2x, respectively, and their product is -2 * 2x = -4x.
Add all these up:
6x + 2x² + (-12) + (-4x) = 2x² + 2x - 12
Clearly, 2x² + 2x - 12 is NOT the same as 4x² + 10x - 6, so (2x - 1)(2x + 6) is not equal to (x - 2)(6 + 2x).
Hope this helps!
Answer:
4x² + 10x - 6
Not equal
Step-by-step explanation:
(2x - 1)(2x + 6)
4x² - 2x + 12x - 6
4x² + 10x - 6
(1x - 2)(6 + 2x)
6x - 12 + 2x² - 4x
2x² + 2x - 12
Not equal
Help me!!!!!!.......
Answer:
D
Step-by-step explanation:
The highest point is the vertex, (-3,5), making all y-values less than or equal to 5.
A frame maker is hired by an art museum to make a special frame for a large rectangle painting. The painting is 3 times as long as it is tall.The expression 2(x+3x) represents the perimeter of the painting, where x represents the length of the short side of the painting in feet. What is the total feet of framing needed if the short side of the painting measures 2.6 feet?
We have been given that the painting is 3 times as long as it is tall.The expression [tex]2(x+3x)[/tex] represents the perimeter of the painting, where x represents the length of the short side of the painting in feet.
To find the the amount of framing needed when short side of the painting measures 2.6 feet, we will substitute [tex]x=2.6[/tex] in our given expression.
We can simplify our expression as:
[tex]2(x+3x)=2(4x)[/tex]
[tex]2(4x)=2(4\times 2.6)[/tex]
[tex]2(4x)=2(10.4)[/tex]
[tex]2(4x)=20.8[/tex]
Therefore, a total of 20.8 feet of framing is needed.
By using the given expression 2(x+3x) and substituting the short side measurement of 2.6 feet, we find that the total framing needed is 20.8 feet for the large rectangle painting.
Explanation:To calculate the total framing needed for the painting, we start by using the expression 2(x+3x), which represents the perimeter of the painting. Given that the short side (x) of the painting measures 2.6 feet, we substitute x with 2.6 feet in the expression, resulting in 2(2.6 feet + 3(2.6 feet)), which simplifies to 2(2.6 feet + 7.8 feet). This gives us 2(10.4 feet), equaling 20.8 feet of framing that is needed.
The dimensions of the painting are based on the fact that the painting is three times as long as it is tall.
The short side is the height of the painting, and the long side, therefore, is 3 times the short side. Since the painting is a rectangle, we apply the formula for the perimeter of a rectangle, which is P = 2(length + width), to get the overall framing length.
how do you write 6.1 x 10^2 in standard form
The expression [tex]6.1 \times 10^2[/tex] in standard form is 610
How to write the expression in standard form
From the question, we have the following parameters that can be used in our computation:
[tex]6.1 \times 10^2[/tex]
To write [tex]6.1 x 10^2[/tex] in standard form, we need to convert it into a regular number.
using the above as a guide, we have the following:
[tex]6.1 * 10^2 = 6.1 * 100[/tex]
Evaluate
[tex]6.1 * 10^2 = 610[/tex]
Hence, the expression in standard form is 610
Which is more, 2 pound or 22 ounces
Answer:
2 pounds. Two pounds is 32 oz. so if 22 oz. is less than 32 (which it obviously is), 2 pounds is more.
Answer:
2 pounds
Step-by-step explanation:
What is the value of the expression-7 3/4 + 3 1/2
Answer:
45/4 or 11.25 or 11 1/4
Step-by-step explanation:
Answer:
Step-by-step explanation:-15/4
-15/4
Write this word sentence as an inequality. A number y is greater than 1 and is less than or equal to 8 .
Answer:
1<y≤8
Step-by-step explanation:
step 1
The number is y and it is greater than one.
The sign for greater than in mathematics is '>'
Therefore, we can write
y>1
And it means 1 is less than y
Less than = <
1<y
Step 2
y is less than or equal to 8. In mathematics, the 'less than or equal to' sign is '≤'
Therefore, we can write
y≤8
Step 3
We then combine these two inequalities
1<y≤8
Final answer:
The inequality 1 < y ≤ 8 represents a number y that is greater than 1 and less than or equal to 8.
Explanation:
An inequality representing the statement 'A number y is greater than 1 and is less than or equal to 8' can be expressed as:
1 < y ≤ 8
This inequality signifies that y is greater than 1 (1 < y) and at the same time, less than or equal to 8 (y ≤ 8), fulfilling both conditions simultaneously.
Kevin and Jenny are making plaster. Kevin mixes 3 cups of water with 4 pounds of plaster powder. Complete the ratio table. How much water will Kevin need for 20 pounds of plaster?
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
Answer:
x^2 + (y – 3)^2 = 36
Step-by-step explanation:
The standard equation of a circle with center at (h, k) and radius r is
(x - h)^2 + (y - k)^2 = r^2.
If the center lies on the y-axis, then h = 0: (x - 0)^2 + (y - k)^2 = r^2
If the circle diameter is 12, then the circle radius is 6, and so r^2 = 36
So, among the given equations, your
x^2 + (y – 3)^2 = 36 is correct (but only if you use " ^ " for exponentiation).
The equations that represent circles with a diameter of 12 units and a center on the y-axis are x² + (y - 6)² = 36 and x² + (y + 6)² = 36.
Explanation:The equations that represent circles with a diameter of 12 units and a center on the y-axis are:
x² + (y - 6)² = 36x² + (y + 6)² = 36To determine if an equation represents a circle, we need to check if the equation follows the standard form of a circle equation, which is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius. In this case, since the center lies on the y-axis, the x-coordinate of the center is 0, and we only need to consider the y-coordinate.
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What is the equation of the line that is perpendicular to and
has the same y-intercept as the given line?
y= 4x+1
(50)
y= 4x+5
tos -
32
2
3
4
5
6
y = 5x + 1
5x + 5
Answer:
y = (-¼)x + 1
Step-by-step explanation:
y = 4x + 1
Slope of the perpedicular:
m = -¼
Equation:
y = (-¼)x + 1
4y = -x + 4
Right △EFG has its right angle at F, EG=8 , and FG=2 .
What is the value of the trigonometric ratio of an angle of the triangle?
tan E
sin G
sec G
In triangle EFG, the right angle is at F. Using the Pythagorean theorem, we can find the length of the hypotenuse and use it to calculate the trigonometric ratios.
Explanation:In triangle EFG, the right angle is at F. Given that EG = 8 and FG = 2, we can use the Pythagorean theorem to find the length of EF. Using the formula a^2 + b^2 = c^2, where a and b are the lengths of the legs and c is the length of the hypotenuse, we can calculate that EF = sqrt((EG^2) + (FG^2)) = sqrt((8^2) + (2^2)) = sqrt(64 + 4) = sqrt(68).
To find tan E, we can use the ratio of the opposite side (FG) to the adjacent side (EG). tan E = FG/EG = 2/8 = 1/4.
To find sin G, we can use the ratio of the opposite side (FG) to the hypotenuse (EF). sin G = FG/EF = 2/sqrt(68).
To find sec G, we can use the ratio of the hypotenuse (EF) to the adjacent side (EG). sec G = EF/EG = sqrt(68)/8.
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What is the value of (Negative three-fourths) Superscript negative 4?
The value of (-3/4[tex])^{-4[/tex] is 256/81.
What is Exponents and Power?Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.
For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as [tex]3^4[/tex], where 4 is the exponent and 3 is the base. The whole expression 34 is said to be power.
We have to find the value of (-3/4[tex])^{-4[/tex]
First of all make the power positive by reciprocate the number
= (-3/4[tex])^{-4[/tex]
= (-4/ 3 [tex])^4[/tex]
Now, expanding the number we get
= (-4 x -4 x -4 x -4) / (3 x 3 x 3 x 3)
= 256 / 81
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test achievement series.com/asot.aspx
Alice wants her cat to lose some weight. If she wants her cat to lose weight at a rate of 2 lbs per month, which graph represents this rate of loss?
1
Cat Weight Loss
Cat Weight Loss
x
Weight (lbs)
öö
Weight (lbs)
0
5
# of Months
1 2 3 4
#of Months
Cat Weight Loss
Cat Weight Loss
L
ū8
right (lbs
ight (lbs)
What are the solutions to the equation x2 + 4x + 5 = 0?
please help PLEASE
Which equations are equal to this equation? 14(8x + 56) = 20
Answer:
x = - 191/28
Step-by-step explanation:
14 (8x + 56) = 20
112x + 784 = 20
112x = 20 - 784
112x = - 764
x = - 764/112
x = - 191/28
Answer:
Here are a few equivalent equations:
112x + 784 = 20
112x = -764
x = -6.82
Step-by-step explanation:
14(8x + 56) = 20
Multiply
112x + 784 = 20
Subtract 784 from both sides of the equation
112x = -764
x = -6.82
Hope this was useful to you!
What are the coordinates of the image ABC after a dilation with center (0,0) and a scale factor of 1/2? HELP ASAP
Answer:
A: 1,1 B: 2,3 C;3,1
Step-by-step explanation:
Divide each number by 1/2 or times by .5
The temperature at the top of a mountain is 10.8°C less than the
temperature at the base of the mountain. If the temperature at the
base is -4.4°C. what is the temperature at the top? *
Answer:
-15.2°C
Step-by-step explanation:
-4.4 - 10.8 = -15.2
Hope this helps <3
The temperature at the top of the mountain is -15.2°C.
The solution to the problem:
Given:
The temperature at the base of the mountain is -4.4°C.
The temperature at the top of the mountain is 10.8°C less than the temperature at the base of the mountain.
Objective:
Determine the temperature at the top of the mountain.
Solution:
Let x be the temperature at the top of the mountain. We know that the temperature at the top of the mountain is 10.8°C less than the temperature at the base of the mountain, so we can write the following equation:
x = -4.4 - 10.8
Simplifying the right side of the equation, we get:
x = -15.2°C
Find the area of the figure. *
12 yd
12 yd
Answer:
144 yards
Step-by-step explanation:
Multiply 12 yd by 12 yd =
144 yards
Answer: The answer is 144yd squared
Step-by-step explanation:
Pia a circumference of approssimately 75 inches
What is the approximate length of the radius,
for 2. Round to the nearest inch
Use 3.14
12 inches
24 inches
38 inches
46 inches
Answer:
radius: 12 inches or OPTION A
Step-by-step explanation:
C = 2r × 3.14
75 = 2r × 3.14
23.885 = 2r
r = 11.94
Please help!
I really can't figure it out.
Answer:
x = 5 (pleaaaaaase give branliest)
Step-by-step explanation:
An equilateral triangle is a triangle that has all congruent sides
This means that 30 = 4x + 10
30 - 10 = 4x
20 = 4x
20/4 = x
x = 5
Hope this helps
Answer:
x=5
Step-by-step explanation:
All sides are equal length because it is an equilateral triangle.
30 = 4x+10
Subtract 10 from each side
30-10= 4x+10-10
20 =4x
Divide each side by 4
20/4 = 4x/4
5 =x
Consider the data set:
20, 30, 39, 44, 52
How much does 52 deviate from the mean?
Answer:
15
Step-by-step explanation:
mean = 20 + 30 + 39 + 44 + 52 /5
mean = 185 ÷ 5
mean = 37
52 - 37 = 15
The mean of the data set is 37. The number 52 deviates from the mean by 15. Key concepts include mean, deviation, and data set.
Explanation:The first step in answering the question 'How much does 52 deviate from the mean?' is to calculate the mean (also called the average) of the data set. We do this by adding together each of the numbers in the data set and then dividing by the number of elements. The calculation looks like this: (20 + 30 + 39 + 44 + 52) / 5 = 37. Then, to determine how much 52 deviates from the mean, subtract the mean from 52. This gives us: 52 - 37 = 15. So, 52 deviates from the mean by 15. Mean, deviation, and data set are key mathematical concepts related to this question and answer.
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Find the area of the triangle that has a base of 16 yd and a height of 9 yd.
72 yd2
144 yd2
25 yd2
50 yd2
negative 8/9 divided by 2/3
Answer:
[tex]\frac{4}{3}[/tex]
Step-by-step explanation:
Step 1: Divide
[tex]\frac{8}{9} / \frac{2}{3}[/tex]
[tex]\frac{8}{9} * \frac{3}{2}[/tex]
[tex]\frac{8 * 3}{9 * 2}[/tex]
[tex]\frac{24/6}{18/6}[/tex]
[tex]\frac{4}{3}[/tex]
Answer: [tex]\frac{4}{3}[/tex]
solve the following equation for x: 6( 4x + 5) = 3(x + 8) + 3. round to the nearest hundredth.
Answer:
-0.14
Step-by-step explanation:
First eliminate the parenthesis:
6( 4x + 5) = 3(x + 8) + 3 =>
24x + 30 = 3x + 24 + 3
Then group x terms on the left and constants on the right
24x - 3x = 24 + 3 - 30
21x = -3
Divide by 21 and simplify:
x = -3/21 = -1/7 ≈ -0.14
Answer:
- 1/7
Step-by-step explanation:
6(4x + 5) = 3(x + 8) + 3
Expand the brackets
6 X 4x + 6 x 5 = 3 X x + 3 X 8 + 3
24x + 30 = 3x + 24 + 3
24x + 30 = 3x + 27
Subtract 30 from both sides to eliminate 30 on the left side
24x + 30 - 30 = 3x + 27 - 30
24x = 3x - 3
Subtract 3x from both sides to eliminate bring all variables to one side
24x - 3x = 3x - 3x - 3
21x = -3
Divide both sides by 21 to isolate x
21x/21 = -3/21
x = -1/7
x = - 1/7