Question

Solve each equation. Check your solution.

$-11=\frac{a-5}{6}$

Short answer

The solution of the given equation is $a=-61$.

Step-by-step solution

Step 1. Write the given equation.

The given equation is “$-11=\frac{a-5}{6}$”.

Step 2. Solve the given equation.

Solving,

$-11=\frac{a-5}{6}$ (Given equation)

$-11\times 6=\frac{a-5}{6}\times 6$ (Multiply both sides by 6)

$-66=a-5$ (Simplify)

$-66+5=a-5+5$ (Add 5 to both sides)

$-61=a$ (Simplify)

$a=-61$ (Write the variable on the left-hand side)

So, $a=-61$is the solution of the given equation.

Step 3. Check the obtained solution.

Put $a=-61$in the given equation $-11=\frac{a-5}{6}$to get,

$\begin{array}{l}-11=\frac{-61-5}{6}\\ -11=\frac{-66}{6}\\ -11=-11\end{array}$

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.