Question

Solve each equation. Check your solution. (Lesson 2-4)

$8p+3=5p+9$

Short answer

$p=2$ is the solution of the given equation.

Step-by-step solution

Step 1. Given equation.

$8p+3=5p+9$

Step 2. Description of step.

To solve the given equation first take the like terms on one side, and then simplify as:

$$\begin{gathered} 8p+3=5p+9 \\ 8p-5p=9-3 \\ \Rightarrow 3p=6 \\ \Rightarrow p=\frac{6}{3} \\ \Rightarrow p=2 \end{gathered}$$

Thus, $p=2$.

Step 3. Check solution.

In order to check the solution, put the value of p back in the given equation and see if it satisfies the equation, i.e. of left hand side is equals to right hand side, as:

$$\begin{gathered} 8p+3=5p+9\le \\ \Rightarrow 8\left(2\right)+3=5\left(2\right)+9 \\ \Rightarrow 16+3=10+9 \\ \Rightarrow 19=19 \\ \Rightarrow \text{true} \end{gathered}$$

Hence, the solution $p=2$ satisfies the equation.