Question

Solve the equation and check the solution.

$7p-4=3\left(4+5p\right)$

Short answer

The solution is $p=\frac{8}{11}$.

Step-by-step solution

Step 1- Consider the equation.

Consider the equation $7p-4=3\left(4-5p\right)$.

Simplify the equation as follows:

$\begin{array}{l}7p-4=3(4-5p)\\ 7p-4=12-15p\end{array}$

Step 2- Step description.

Now, simplify the equation obtained as follows:

$\begin{array}{c}7p-4=12-15p\\ 7p+15p=12+4\\ 22p=16\end{array}$

Step 3- Step description.

Divide both sides of the equation by 22.

$\begin{array}{l}22p=16\\ p=\frac{16}{22}\end{array}$

Simplify the equation further.

$\begin{array}{l}p=\frac{16}{22}\\ p=\frac{8}{11}\end{array}$

Therefore, the solution is $p=\frac{8}{11}$.

Step 4- Verify the solution.

Substitute $p=\frac{8}{11}$ in the equation and simplify as follows:

$\begin{array}{c}7p-4=3(4-5p)\\ 7\left(\frac{8}{11}\right)-4=3(4-5\left(\frac{8}{11}\right))\\ \frac{56}{11}-4=12-\frac{120}{11}\\ \frac{56-44}{11}=\frac{132-120}{11}\\ \frac{12}{11}=\frac{12}{11}\end{array}$

Since the left-hand side of the equation is equal to the right-hand side of the equation, therefore, the solution is $p=\frac{8}{11}$.