Question

Davon's solution to the equation -2(x - 5) + 3 = -4 is shown below.

-2(x - 5) + 3 = -4

Step 1 -2x - 5 + 3= -4
Step 2 -2x - 2 = -4
Step 3 -2x = -2
Step 4 x = -1

In which step did the first mistake occur?

Step 1

Step 4

Step 2

Step 3

Answer 1

(a) Step 1

Explanation:

The first step to solving the equation is to eliminate parentheses. That involves use of the distributive property.

Devon's solution shows two common mistakes in the first step.

The distributive property tells you ...

a(b +c) = ab +ac

-2(x -5) = (-2)(x) +(-2)(-5) = -2x +10

Devon missed the product with the second term, and also got its sign wrong.

The first mistake occurred in Step 1.

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Additional comment

The solution should look like ...

1. -2x +10 +3 = -4
2. -2x +13 = -4
3. -2x = -17
4. x = 8.5
5. check: -2(8.5 -5) +3 = -4 . . . . true