Question

Solve the inequality. Graph your solution.

$\mathbf{14}\mathbf{p}\mathbf{-}\mathbf{5}\ge \mathbf{-}\mathbf{3}\mathbf{p}\mathbf{+}\mathbf{114}$

Short answer

Solution of the inequality is $p\ge 7$.

Step-by-step solution

Step 1. Solve the inequality

$14p-5\ge -3p+114$

Add 3p and 5 both the sides.

$\begin{array}{c}14p-5+3p+5\ge -3p+114+3p+5\\ 17p\ge 119\end{array}$

Divide both sides by 17.

$\begin{array}{c}p\ge \frac{119}{17}\\ p\ge 7\end{array}$

Step 2. Graph the inequality

The solution of the inequality is $p\ge 7$.

That means, all values $p\ge 7$ satisfy the inequality. So, the graph can be given as shown below.

Step 3. Check the solution

To check the solution, take any random number, $p\ge 7$ and substitute in the original inequality and observe the result.

Take $p=10$.

Then,

$\begin{array}{c}14\times 10-5\ge -3\times 10+114\\ 140-5\ge -30+114\\ 135\ge 84\end{array}$

The result $135\ge 84$ is true. So, the solution $p\ge 7$ is correct.