Question

Solve the inequality. Graph the solution on the number line and write the solution in the interval notation

$9p>14p-18$

Short answer

The solution graph is$p<\frac{18}{5}$

$\left(-\infty ,\frac{18}{5}\right)$

Step-by-step solution

Step 1. Given information.

The following inequality is given:

$9p>14p-18$

Step 2. Solving the inequality.

Subtracting $14p$from both sides of the inequality, the following can be obtained:

$9p-14p>14p-18-14p$

Simplify:

$-5p>-18$

Diving both sides by $-5$(this will reverse the inequality as -5 is negative):

$\frac{-5p}{-5}<\frac{-18}{-5}$

Solution:

$p<\frac{18}{5}$

Step 3. Graphing the solution on the number line

The graph of the inequality on the number line is presented below:

Step 4. Writing the solution in the interval notation

The solution of the inequality in the interval notation can be expressed as

$\left(-\infty ,\frac{18}{5}\right)$