Question

Solve the inequality. Graph and check your solution.

$\mathbf{6}\mathbf{+}\mathbf{y}\ge \mathbf{2}\mathbf{y}\mathbf{-}\mathbf{3}$

Short answer

Solution of the inequality is $y\le 9$.

Step-by-step solution

Step-1- Solve the inequality

$6+y\ge 2y-3$

Subtract y and add 3 to both the sides.

$\begin{array}{c}6+y+3-y\ge 2y-3-y+3\\ 9\ge y\\ y\le 9\end{array}$

Step-2- Graph the inequality

The solution of the inequality is$y\le 9$.

That means, all values $y\le 9$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,$y\le 9$and substitute in the original inequality and observe the result.

Take$y=0$.

Then,

$\begin{array}{c}6+0\ge 2\times 0-3\\ 6\ge 0-3\\ 6\ge -3\end{array}$

The result $6\ge -3$is true. So, the solution$y\le 9$ is correct.