Question

Solve the inequality. Graph your solution.

$\mathbf{19}\ge \frac{\mathbf{x}}{\mathbf{90}}\mathbf{-}\mathbf{25}$

Short answer

Solution of the inequality is $x\le 3960$.

Step-by-step solution

Step 1. Solve the inequality

$19\ge \frac{x}{90}-25$

Add 25 both the sides.

$\begin{array}{c}19+25\ge \frac{x}{90}-25+25\\ 44\ge \frac{x}{90}\end{array}$

Multiply both sides by 90.

$\begin{array}{c}44\ge \frac{x}{90}44\times 90\ge \frac{x}{90}\times 90\\ 3960\ge x\\ x\le 3960\end{array}$

Step 2. Graph the inequality

The solution of the inequality is $x\le 3960$.

That means, all values $x\le 3960$ 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, $x\le 3960$ and substitute in the original inequality and observe the result.

Take $x=0$.

Then,

$\begin{array}{c}19\ge \frac{0}{90}-25\\ 19\ge 0-25\\ 19\ge -25\end{array}$

The result $19\ge -25$ is true. So, the solution $x\le 3960$ is correct.