Question

Solve each equation. Check your solution.

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

Short answer

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

Step-by-step solution

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.