Q11. - Algebra 1

Question

Solve each equation. Check your solution.

$2m-13=-8m+27$

Step-by-Step Solution

Answer

The solution of the given equation is $m=4$.

Step 1. Write the given equation.

The given equation is “$2m-13=-8m+27$”.

Step 2. Solve the given equation.

Solving,

$2m-13=-8m+27$  (Given equation)

$2m-13+8m=-8m+27+8m$  (Add $8m$ to both sides)

$10m-13=27$  (Simplify)

$10m-13+13=27+13$  (Add 13 to both sides)

$10m=40$  (Simplify)

$\frac{10m}{10}=\frac{40}{10}$  (Divide both sides by 10)

$m=4$  (Simplify)

So, $m=4$ is the solution of the given equation.

Step 3. Check the obtained solution.

Put $m=4$ in the given equation $2m-13=-8m+27$ to get,

$\begin{array}{l}2\left(4\right)-13=-8\left(4\right)+27\\ 8-13=-32+27\\ -5=-5\end{array}$

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.