Question

Solve the inequality. Graph and check your solution.

$\mathbf{7}\ge \mathbf{5}\mathbf{x}\mathbf{-}\mathbf{3}$

Short answer

Solution of the inequality is $x\le 2$.

Step-by-step solution

Step-1- Solve the inequality

$\begin{array}{c}7\ge 5x-3\\ 7+3\ge 5x-3+3\left(\text{Add3onbothsides}\right)\\ 10\ge 5x\\ \frac{10}{5}\ge x\left(\text{Dividebothsidesby4}\right)\\ 2\ge x\\ x\le 2\end{array}$

Step-2- Graph the inequality

The solution of the inequality is$x\le 2$.

That means, all values $x\le 2$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,$x\le 2$and substitute in the original inequality and observe the result.

Take$x=0$.

Then,

$\begin{array}{c}7\ge 5\times 0-3\\ 7\ge 0-3\\ 7\ge -3\end{array}$

Observe that 7 is greater than -3. So, the result is true and hence the solution is correct.