Question

Solve the inequality. Graph your solution.

$\frac{\mathbf{x}\mathbf{-}\mathbf{2}}{\mathbf{3}}\mathbf{>}\mathbf{4}$

Short answer

Solution of the inequality is $x>14$.

Step-by-step solution

Step 1. Solve the inequality

$\frac{x-2}{3}>4$

Multiply both sides by 3.

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

Add 2 on both sides.

$\begin{array}{c}x-2+2>12+2\\ x>14\end{array}$

Step 2. Graph the inequality

The solution of the inequality is $x>14$.

That means, all values $x>14$ 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, $x>14$ and substitute in the original inequality and observe the result.

Take $x=17$.

Then,

$\begin{array}{c}\frac{17-2}{3}>4\\ \frac{15}{3}>4\\ 5>4\end{array}$

The result $5>4$ is true. So, the solution $x>14$ is correct.