Question

Solve each equation. Check your solution. (Lesson 2-3)

$\frac{a}{7}-3=-2$

Short answer

The solution of the given equation is $a=7$.

Step-by-step solution

Step 1. Write the given equation.

The given equation is “$\frac{a}{7}-3=-2$”.

Step 2. Solve the given equation.

Solving,

$\frac{a}{7}-3=-2$ (Given equation)

$\frac{a}{7}-3+3=-2+3$ (Add 3 to both sides)

$\frac{a}{7}=1$ (Simplify)

$\frac{a}{7}\times 7=1\times 7$ (Multiply both sides by 7)

$a=7$ (Simplify)

So, $a=7$is the solution of the given equation.

Step 3. Check the obtained solution.

Put $a=7$in the given equation $\frac{a}{7}-3=-2$to get,

$\begin{array}{l}\frac{7}{7}-3=-2\\ 1-3=-2\\ -2=-2\end{array}$

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.