Question 1

Which property is used to move all variable terms to one side and all constant terms to the other side when solving $$2(x - 32) = 10x$$?

Accepted Answer

The addition property of equality

Question 2

What is the first step in solving the equation $$2(x - 32) = 10x$$?

Accepted Answer

Apply the distributive property to remove parentheses

Question 3

After applying the distributive property to $$2(x - 32)$$, what is the resulting expression?

Accepted Answer

$$2x - 64$$

Question 4

Which equation correctly represents the result after subtracting $$2x$$ from both sides of $$2x - 64 = 10x$$?

Accepted Answer

$$2x - 64 = 10x - 2x$$

Question 5

What is the value of $$x in $$the equation $$-64 = 8x$$?

Accepted Answer

$$x = -8$$

Question 6

Which property is used to isolate $$x in $$the equation $$-64 = 8x$$?

Accepted Answer

The multiplication property of equality

Question 7

If you substitute $$x = -8$$ into the original equation $$2(x - 32) = 10x$$, what is the left side of the equation?

Accepted Answer

$$-80$$

Question 8

Which of the following best describes the solution set for the equation $$2(x - 32) = 10x$$?

Accepted Answer

$$\{-8\}$$

Question 9

What is the result of $$2(-8 - 32)$$?

Accepted Answer

$$-80$$

Question 10

Which step verifies that $$x = -8 is a $$solution to $$2(x - 32) = 10x$$?

Accepted Answer

Substitute $$x = -8$$ into the equation and check if both sides are equal

Question 11

Which real-world scenario could be modeled by the equation $$2(x - 32) = 10x$$?

Accepted Answer

A company pays $$2 for each item produced after a fixed cost of 32$, and the total cost equals 10$ times the number of items produced.

Question 12

If the equation $$2(x - 32) = 10x$$ represents the balance between two investment strategies, what does $$x = -8$$ indicate?

Accepted Answer

The strategies break even when the investment is $$-8$$ units (possibly a loss or debt).

Question 13

Which of the following is NOT a correct step in solving $$2(x - 32) = 10x$$?

Accepted Answer

Add $$32 to $$both sides to get $$2x = 10x + 32$$

Question 14

If you made a mistake and divided both sides of $$2x - 64 = 10x by$$ $$2$$ instead of subtracting $$2x$$, what equation would you get?

Accepted Answer

$$x - 32 = 5x$$

Solving Linear Equations with Variable Terms on Both Sides

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