Question

Maricella solves for x in the equation 4 x minus 2 (3 x minus 4) + 4 = negative x + 3 (x + 1) + 1. 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?

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.

Answer 1

A. The multiplication that takes place while distributing comes before addition and subtraction in order of operations.

Explanation:

You want to know the error that adding -4+4 on the left and 1+1 on the right represents in the solution of the equation ...

• 4x -2(3x -4) +4 = -x +3(x +1) +1

Solution

The correct solution procedure would be to eliminate the parentheses using the distributive property as a first step:

4x -6x +8 +4 = -x +3x +3 +1

Comparing this to Maricella's first step, we see that she ignored the step of using the distributive property to multiply the constants inside parentheses by the factor outside. The appropriate description of Maricella's mistake is ...

A. The multiplication that takes place while distributing comes before addition and subtraction in order of operations.

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Additional comment

Adding like terms would give ...

-2x +12 = 2x +4

8 = 4x . . . . . . . . . . . add 2x-4 to both sides

2 = x . . . . . . . . . . divide by 4

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