Question

question
choose the justification for each step in the solution to the given equation.

step	statement	reason
2	\\(-2x - 7 = -15\\)	\\(\boldsymbol{\

abla}\\) |

3	\\(-2x - 7 + 7 = -15 + 7\\)	addition property of equality<br>subtraction property of equality<br>multiplication property of equality<br>division property of equality<br>combining like terms
4	\\(-2x = -8\\)
5	\\(\frac{-2x}{-2} = \frac{-8}{-2}\\)
6	\\(x = 4\\)

Explanation:

Step1: Analyze Step 2

In Step 1, we have \(\frac{1}{4}x - \frac{9}{4}x - 7=-15\). To get to Step 2 (\(-2x - 7=-15\)), we combine the like terms \(\frac{1}{4}x\) and \(-\frac{9}{4}x\).
\(\frac{1}{4}x-\frac{9}{4}x=\frac{1 - 9}{4}x=\frac{-8}{4}x=-2x\)
So the operation here is combining like terms.

Step2: Confirm the Reason

For Step 2, since we combined the \(x\)-terms (\(\frac{1}{4}x\) and \(-\frac{9}{4}x\)) to get \(-2x\), the justification is "combining like terms".

Answer:

For Step 2, the reason is "combining like terms".