Question

Tell whether the given number is a solution of$\mathbf{5}\mathbf{x}\mathbf{-}\mathbf{10}\mathbf{>}\mathbf{2}\mathbf{x}\mathbf{+}\mathbf{4}$.

4

Short answer

No, $x=4$is not a solution.

Step-by-step solution

Step-1- Solve the inequality

$5x-10>2x+4$

First add 10 and then subtract 2x at both side

$\begin{array}{c}5x-10+10-2x>2x+4-2x+10\\ 3x>14\end{array}$

Divide by 3.

$\begin{array}{c}x>\frac{14}{3}\\ x>4.66\end{array}$

Step-2- Graph the inequality

The solution of the inequality is$x>4.66$.

That means, all values$x>4.66$ satisfy the inequality. So, the graph can be given as shown below.

Step-3- Check the solution

To check the solution, substitute$x=4$ in the original inequality and observe the result.

$\begin{array}{c}5\times 4-10>2\times 4+4\\ 20-10>8+4\\ 10>12\end{array}$

The result$10>12$ is not true. So,$x=4$ is not a solution of the inequality.