Q18. - Algebra 1

Question

Solve each equation. Check your solution.

$5\left(g+8\right)-7=103$

Step-by-Step Solution

Answer

The solution of the given equation is $g=14$.

Step 1. Write the given equation.

The given equation is “$5\left(g+8\right)-7=103$”.

Step 2. Solve the given equation.

Solving,

$5\left(g+8\right)-7=103$  (Given equation)

$5\left(g+8\right)-7+7=103+7$  (Add 7 to both sides)

$5\left(g+8\right)=110$  (Simplify)

$\frac{5\left(g+8\right)}{5}=\frac{110}{5}$  (Divide both sides by 5)

$g+8=22$  (Simplify)

$g+8-8=22-8$  (Subtract 8 from both sides)

$g=14$  (Simplify)

So, $g=14$ is the solution of the given equation.

Step 3. Check the obtained solution.

Put $g=14$ in the given equation $5\left(g+8\right)-7=103$ to get,

$\begin{array}{l}5\left(14+8\right)-7=103\\ 5\left(22\right)-7=103\\ 110-7=103\\ 103=103\end{array}$

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.