11. A student solved the equation: x + 2(x + 1) = 17

Question

Step one: x +2x + 2 = 17
Step two: 3x + 2 = 17
Step three: 3x = 15
Step four: x = 45

Identify the property used to arrive at Step one.
What step includes a mistake made from the previous step?
What should have been the correct answer for x?

Answer 1

1. The property used to arrive at Step one is the Distributive Property. The student distributed the 2 into the expression \( (x + 1) \) in the equation \( 2(x + 1) \) to get \( 2x + 2 \).

2. The mistake made from the previous step appears in Step four. The student incorrectly solved for \( x \). After correctly simplifying to \( 3x = 15 \), they made an arithmetic error when dividing by 3.

3. The correct answer for \( x \) should be \( x = 5 \) (since \( 3x = 15 \) leads to \( x = 15 / 3 = 5 \)).