AnswersSRC 2022 MJ Grade 8 Pre-Algebra Q1Solving Multistep Equations with Variables on Both Sides

Solving Multistep Equations with Variables on Both Sides Answers

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1
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What is the value of x in the equation ? Write your solution in decimal form.

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Answer not available
2
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Carey solves the equation by applying the distributive property on both sides of the equation. The result is . Carey then wants to combine like terms. Which are the terms Carey should combine?

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A
8x + 2x
B
–4 + 5 + 3 + 2
C
–4 + 5 and 3 + 2
D
4 + 5 and 3 + 2
3

Maricella solves for x in the equation . She begins by adding –4 + 4 on the left side of the equation and 1 + 1 on the right side of the equation. Which best explains why Maricella’s strategy is incorrect?

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A
The multiplication that takes place while distributing comes before addition and subtraction in order of operations.
B
In order to combine like terms on one side of the equation, the inverse operation must be used.
C
When the problem is worked in the correct order, the numbers that Maricella added are not actually like terms.
D
Maricella did not combine all three constants on both sides of the equation; she combined only two.
4

What is the value of x in the equation ?

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Answer not available
5

In order to solve for the variable in the equation , Jaleesa begins by applying the distributive property, then combines like terms. Which equation is the result of these steps?

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A
7 x + 6 = 6 x minus 3
Option A
B
2 x + 6 + 5 x = 6 x minus 3
Option B
C
2 x + 3 + 5 x = 6 x minus 1
Option C
D
7 x + 3 = 6 x minus 1
Option D
6

What is the solution to the equation ?x =

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Answer not available
7

In order to solve for the variable in the equation , Mikel first applies the distributive property. Which equation is a result of this step?

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A
1 minus x + 2 + 2 x = 10 x minus 5 minus x
Option A
B
1 minus x minus 2 + 2 x = 10 x minus 25 minus x
Option B
C
1 minus x minus 1 + 2 x = 10 x minus 25 minus x
Option C
D
1 minus x minus 1 + 2 x = 10 x minus 5 minus x
Option D
8

In order to solve for the variable in the equation , Giovanni first applies the distributive property. Which equation is a result of this step?

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A
8 x + 3 + 4 = 3 x minus 2 x + 4
Option A
B
8 x + 6 + 4 = 3 x minus 2 x minus 4
Option B
C
6 x + 5 + 4 = 3 x minus x + 3
Option C
D
6 x + 3 + 4 = 3 x minus x + 4
Option D
9

Which is a reasonable first step that can be used to solve the equation ?

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A
Combine like terms, 3 and 5, on the right side of the equation.
B
Distribute 2 to (x + 6) and 3 to (x – 4).
C
Distribute 2 to x on the left side of the equation and 3 to x on the right side of the equation.
D
Apply the subtraction property of equality to move the 6 from the left side of the equation to the right side.
10

To solve the equation, Lorie applies the distributive property, combines like terms, then applies the addition and subtraction properties of equality to isolate the variable term on one side of the equation and the constant term on the other side. What are the possible coefficients of x after Lorie has completed these steps?

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A
–32 and 2
B
–2 and 32
C
–2 and 2
D
–32 and 32
11

Gwyneth begins solving for x in the equation . After applying the distributive property and combining like terms, which equation will Gwyneth have to solve in order to determine the value of x?

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A
2 x minus 8 = 20 minus 14 x
Option A
B
2 x minus 8 = 20 minus 6 x
Option B
C
2 x minus 4 = 20 + 2 x
Option C
D
2 x minus 4 = 20 minus 6 x
Option D
12

Antoinette solves the linear equation using the steps shown below. Step 1: Step 2: Step 3: Step 4: She checks her solution by substituting –7 for x in the original equation. She determines that her answer is incorrect. Which best describes Antoinette’s error?

Question illustration
A
She distributed incorrectly.
B
She incorrectly combined like terms.
C
She incorrectly applied the addition and subtraction properties of equality.
D
She incorrectly applied the multiplication and division properties of equality.
13

Jorge solves the equation using the steps below. Step 1: Step 2: Step 3: Step 4: Step 5: Jorge verifies his solution by substituting into the original equation for x. He determines that his solution is incorrect. Which best describes Jorge’s error?

Question illustration
A
Jorge distributed incorrectly.
B
Jorge incorrectly combined like terms.
C
Jorge incorrectly applied the addition and subtraction properties of equality.
D
Jorge incorrectly applied the multiplication and division properties of equality.
14

What is the solution to the equation ?

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A
x = 0
Option A
B
x = 4
Option B
C
x = 5
Option C
D
x = 15
Option D
15

Misha solves the equation by applying the distributive property to each side of the equation. The result is . Misha then wants to combine like terms. Which are the terms Misha should combine?

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A
3x – 2x and –8 – 7
B
3x – 2x and 8 – 7
C
3x – 2x + 4x and –6 – 8 – 7
D
3x – 2x – 6 and 4x – 8 – 7

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