Download Solve Linear Equations 1. Which value of x makes the following

Solve Linear Equations
1. Which value of x makes the following equation true?
5(x - 1) = -2x + 37
A. 6
B. 9
C. 7
D. 10
2.
Directions: Drag each equation to the correct location on the model.
Classify each of the equations below according to the number of solutions.
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24x + 12 = 2(12x + 6)
5(x + 8) - 7x = -(2x - 4)
8(x + 7) = 6(x - 4)
2(x + 12) - 2x = 3(x - 2)
5x - 20 = 3(x - 4)
12x + 21 = 3(4x + 6)
3. Which value for x makes the sentence true?
6x - 6 = 2x + 6
A. -3
B. 3
C. 9
D. 5
4.
Directions: Drag each equation to the correct location on the model. Not all equations will be
used.
Finish the calculation below by arranging the steps to solve for x.
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5. Which value for x makes the sentence true?
3x - 2 = 13
A. x = 3
B. x = 15
C. x = 5
D. x = 18
6.
Directions: Drag each image to the correct location on the equation.
Use the terms below to create a linear equation with a solution of x = 10.
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7. Which of the following equations has no real solutions?
A. 6(x - 2) = 6x - 12
B. 6x - 2 = 6x - 2
C. 6(x + 2) = 6(x + 11)
D. 6x - 2 = 12x - 2
8. Solve for x.
A. x = -12
B. x = 65
C. x = 39
D. x = 52
9. Which of the following best describes the solution to the equation below?
7x + 4 = 7x + 4
A. no real solutions
B. infinite real solutions
C. exactly one real solution,
D. exactly one real solution,
10.
Directions: Type the correct answers in each box. Use numerals instead of words. If necessary,
use / for the fraction bar(s).
One yard company charges $10x + $50 a month to mow and edge a lawn. A second company
charges $8x + $60 a month to mow and edge a lawn. Each lawn company also offers additional
services for an extra fee.
Let x represent the number of additional services.
Mr. Mead is comparing the two companies. How many additional services are needed for the
two companies to be the same price?
Mr. Mead needs
Answers
1. A
2. -3. B
additional services for the companies to cost the same price.
4. -5. C
6. -7. C
8. D
9. B
10. --
Explanations
1. Isolate x on one side of the equation to solve.
5(x - 1)
5x - 5
5x - 5 + 2x
7x - 5
7x - 5 + 5
7x
7x ÷ 7
x
=
=
=
=
=
=
=
=
-2x + 37
-2x + 37
-2x + 37 + 2x
37
37 + 5
42
42 ÷ 7
6
2.
Solve each equation.
Since x = 4, then this equation has one real solution.
Since 21 does not equal 18, this equation has no real solutions.
Since x = -40, this equation has one real solution.
Since 40 does not equal 4, this equation has no real solutions.
Since 12 = 12, this equation has infinite real solutions.
Since x = 10, the equation has one real solution.
3. Isolate the variable, x, on one side of the equation to solve.
6x - 6 = 2x + 6
6x - 6 - 2x = 2x + 6 - 2x
4x - 6 = 6
4x - 6 + 6 = 6 + 6
4x = 12
4x ÷ 4 = 12 ÷ 4
x=3
4.
To finish the calculation, start by adding 4 to both sides and combining like terms.
Next, subtract 2x from both sides and combine like terms.
Then, divide both sides of the equation by the coefficient of x, 4.
5. Keep in mind that the goal is to get x by itself.
3x - 2
3x - 2 + 2
3x
3x ÷ 3
x
=
=
=
=
=
6.
Only one equation would have a solution of x = 10.
7. Solve the following equation.
13
13 + 2
15
15 ÷ 3
5
6(x + 2) =
6x + 12 =
6x - 6x =
0
6(x + 11)
6x + 66
66 - 12
54
Since 0 is never equal to 54, no real number would satisfy the equation 6(x + 2) = 6(x + 11).
Therefore, the equation 6(x + 2) = 6(x + 11) has no real solutions.
8. Keep in mind that the goal is to get x by itself.
9. Solve the given equation.
7x + 4 = 7x + 4
7x - 7x = 4 - 4
0=0
So, the lines y = 7x + 4 and y = 7x + 4 coincide.
Therefore, the equation 7x + 4 = 7x + 4 has infinite real solutions.
10.
To determine when the two companies are the same price, set the two expressions equal to each
other and solve for x.
Therefore, Mr. Mead needs 5 additional services for the companies to cost the same price.