Question

Solve the inequality. Graph your solution.

$\frac{\mathbf{x}\mathbf{+}\mathbf{5}}{\mathbf{3}}\le \mathbf{2}$

Short answer

Solution of the inequality is $x\le 1$.

Step-by-step solution

Step 1. Solve the inequality

$\frac{x+5}{3}\le 2$

Multiply both sides by 3.

$\begin{array}{c}\frac{x+5}{3}\times 3\le 2\times 3\\ x+5\le 6\end{array}$

Subtract 5 on both sides.

$\begin{array}{c}x+5-5\le 6-5\\ x\le 1\end{array}$

Step 2. Graph the inequality

The solution of the inequality is $x\le 1$.

That means, all values $x\le 1$ 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, $x\le 1$ and substitute in the original inequality and observe the result.

Take $x=1$.

Then,

$\begin{array}{c}\frac{1+5}{3}\le 2\\ \frac{6}{3}\le 2\\ 2\le 2\end{array}$

The result $2\le 2$ is true. So, the solution $x\le 1$ is correct.