Question

Solve each equation. Check your solution.

$7c+12=-4c+78$

Short answer

The solution of the given equation is $c=6$.

Step-by-step solution

Step 1. Write the given equation.

The given equation is “$7c+12=-4c+78$”.

Step 2. Solve the given equation.

Solving,

$7c+12=-4c+78$ (Given equation)

$7c+12+4c=-4c+78+4c$ (Add $4c$to both sides)

$11c+12=78$ (Simplify)

$11c+12-12=78-12$ (Subtract 12 from both sides)

$11c=66$ (Simplify)

$\frac{11c}{11}=\frac{66}{11}$ (Divide both sides by 11)

$c=6$ (Simplify)

So, $c=6$is the solution of the given equation.

Step 3. Check the obtained solution.

Put $c=6$in the given equation $7c+12=-4c+78$to get,

$\begin{array}{l}7\left(6\right)+12=-4\left(6\right)+78\\ 42+12=-24+78\\ 54=54\end{array}$

Since the value obtained on the left-hand side and right-hand side are equal, the obtained value is indeed a solution of the given equation.