Q19. - Algebra 1

Question

Solve each equation. Check your solution.

$12-\frac{4}{5}\left(x+15\right)=4$

Step-by-Step Solution

Answer

The solution of the given equation is $x=-5$.

Step 1. Write the given equation.

The given equation is “$12-\frac{4}{5}\left(x+15\right)=4$”.

Step 2. Solve the given equation.

Solving,

$12-\frac{4}{5}\left(x+15\right)=4$  (Given equation)

$12-\frac{4}{5}\left(x+15\right)-12=4-12$  (Subtract 12 from both sides)

$-\frac{4}{5}\left(x+15\right)=-8$  (Simplify)

$-\frac{4}{5}\left(x+15\right)\times \left(-\frac{5}{4}\right)=-8\times \left(-\frac{5}{4}\right)$  (Multiply both sides by $-\frac{5}{4}$)

$x+15=10$  (Simplify)

$x+15-15=10-15$  (Subtract 15 from both sides)

$x=-5$  (Simplify)

So, $x=-5$ is the solution of the given equation.

Step 3. Check the obtained solution.

Put $x=-5$ in the given equation $12-\frac{4}{5}\left(x+15\right)=4$ to get,

$\begin{array}{l}12-\frac{4}{5}\left(-5+15\right)=4\\ 12-\frac{4}{5}\left(10\right)=4\\ 12-4\left(2\right)=4\\ 12-8=4\\ 4=4\end{array}$

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.