Question

solve the equation. simplify your answer if possible.
-7(c - 5) + 2 = 9 - (c + 2)
the solution set is { }.

Explanation:

Step1: Expand both sides

First, we expand the left - hand side: \(-7(c - 5)+2=-7c+35 + 2=-7c + 37\)
Then, we expand the right - hand side: \(9-(c + 2)=9 - c-2=7 - c\)
So the equation becomes \(-7c+37 = 7 - c\)

Step2: Move the terms with c to one side

Add \(7c\) to both sides of the equation: \(-7c+7c + 37=7 - c+7c\)
Simplify to get \(37=7 + 6c\)

Step3: Solve for c

Subtract 7 from both sides: \(37-7=7 + 6c-7\)
We have \(30 = 6c\)
Divide both sides by 6: \(c=\frac{30}{6}=5\)

Answer:

\(\{5\}\)