Question

solve the linear equation for c.\
$-32 = c - (-4c + 12)$

Explanation:

Step1: Simplify the right - hand side

First, we simplify the expression \(c-(-4c + 12)\). When we subtract a negative expression, it is equivalent to adding the positive of that expression. So, \(c-(-4c + 12)=c + 4c-12\). Combining like terms \(c+4c = 5c\), so the equation becomes \(-32=5c - 12\).

Step2: Isolate the term with c

We add 12 to both sides of the equation to isolate the term with \(c\). Adding 12 to both sides: \(-32 + 12=5c-12 + 12\). Calculating the left - hand side, \(-32+12=-20\), and the right - hand side simplifies to \(5c\). So we have \(-20 = 5c\).

Step3: Solve for c

We divide both sides of the equation \(-20 = 5c\) by 5. \(\frac{-20}{5}=\frac{5c}{5}\). Calculating the left - hand side, \(\frac{-20}{5}=-4\), and the right - hand side simplifies to \(c\).

Answer:

\(c=-4\)