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

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