Q36. - Algebra 1

Question

Solve each equation. Check your solution.

$5\left[2p-4\left(p+5\right)\right]=25$

Step-by-Step Solution

Answer

The solution of the given equation is $p=-\frac{25}{2}$.

Step 1. Write the given equation.

The given equation is “$5\left[2p-4\left(p+5\right)\right]=25$”.

Step 2. Solve the given equation.

Solving,

$5\left[2p-4\left(p+5\right)\right]=25$  (Given equation)

$\frac{5\left[2p-4\left(p+5\right)\right]}{5}=\frac{25}{5}$  (Divide both sides by 5)

$2p-4\left(p+5\right)=5$  (Simplify)

$2p-4p-20=5$  (Distributive property)

$-2p-20=5$  (Simplify)

$-2p-20+20=5+20$  (Add 20 to both sides)

$-2p=25$  (Simplify)

$\frac{-2p}{-2}=\frac{25}{-2}$  (Divide both sides by $-2$)

$p=-\frac{25}{2}$  (Simplify)

So, $p=-\frac{25}{2}$ is the solution of the given equation.

Step 3. Check the obtained solution.

Put $p=-\frac{25}{2}$ in the given equation $5\left[2p-4\left(p+5\right)\right]=25$ to get,

$\begin{array}{l}5\left[2\left(-\frac{25}{2}\right)-4\left(-\frac{25}{2}+5\right)\right]=25\\ 5\left[-25-4\left(\frac{10-25}{2}\right)\right]=25\\ 5\left[-25-4\left(-\frac{15}{2}\right)\right]=25\\ 5\left[-25-2\left(-15\right)\right]=25\end{array}$

On further simplification,

$\begin{array}{l}5\left[-25+30\right]=25\\ 5\left[5\right]=25\\ 25=25\end{array}$

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.