Question

Solve the inequality. Graph your solution.

$\mathbf{-}\mathbf{3}\le \frac{\mathbf{2}\mathbf{x}\mathbf{+}\mathbf{4}}{\mathbf{4}}$

Short answer

Solution of the inequality is $x\ge -8$.

Step-by-step solution

Step 1. Solve the inequality

$-3\le \frac{2x+4}{4}$

Multiply both sides by 4.

$\begin{array}{c}-3\times 4\le \frac{2x+4}{4}\times 4\\ -12\le 2x+4\end{array}$

Subtract 4 on both sides.

$\begin{array}{c}-12-4\le 2x+4-4\\ -16\le 2x\\ 2x\ge -16\end{array}$

Divide both sides by 2.

$\begin{array}{c}x\ge \frac{-16}{2}\\ x\ge -8\end{array}$

Step 2. Graph the inequality

The solution of the inequality is $x\ge -8$.

That means, all values $x\ge -8$ 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, $x\ge -8$ and substitute in the original inequality and observe the result.

Take $x=1$.

Then,

$\begin{array}{c}-3\le \frac{2\times 0+4}{4}\\ -3\le \frac{0+4}{4}\\ -3\le \frac{4}{4}\\ -3\le 1\end{array}$

The result $-3\le 1$ is true. So, the solution \[x\ge -8\] is correct.