Q34. - Algebra 1

Question

Solve each equation. State any extraneous solutions.

$\frac{\mathbf{6}}{\mathbf{5}}\mathbf{+}\frac{\mathbf{4}\mathbf{p}}{\mathbf{3}}\mathbf{=}\frac{\mathbf{8}\mathbf{p}}{\mathbf{5}}$

Step-by-Step Solution

Answer

The solution of the equation is $\frac{\mathbf{9}}{\mathbf{2}}$.

Step 1. State the concept for observational studies.

The linear equations in one variable is an equation which is expressed in the form of $ax+b=0$, where a and b are two integers, and x is a variable and has only one solution.

Step 2. Solve the equation.

The equation can be solved as follows:

$\begin{array}{c}\frac{6}{5}+\frac{4p}{3}=\frac{8p}{5}\\ \frac{3\left(6\right)+5\left(4p\right)}{15}=\frac{8p}{5}\\ \frac{3\left(6\right)+5\left(4p\right)}{15}\times 15=\frac{8p}{5}\times 15\\ 3\left(6\right)+5\left(4p\right)=8p\times 3\\ 18+20p=24p\\ 18=24p-20p\\ 18=4p\\ p=\frac{18}{4}\\ p=\frac{9}{2}\end{array}$

Step 3. Check the solution.

To check the solution, substitute $p=\frac{9}{2}$ for in the original equation,

$\begin{array}{c}\frac{6}{5}+\frac{4p}{3}=\frac{8p}{5}\\ \frac{6}{5}+\frac{4\left(\frac{9}{2}\right)}{3}=\frac{8\left(\frac{9}{2}\right)}{5}\\ \frac{6}{5}+\frac{2\left(9\right)}{3}=\frac{4\left(9\right)}{5}\\ \frac{6}{5}+\frac{18}{3}=\frac{36}{5}\\ \frac{6}{5}+6=\frac{36}{5}\\ \frac{6+6\left(5\right)}{5}=\frac{36}{5}\\ \frac{6+30}{5}=\frac{36}{5}\\ \frac{36}{5}=\frac{36}{5}\\ LHS=RHS\end{array}$

Since both sides are equal, the equation is correct.