Question

Solve the inequality. Graph your solution.

$\mathbf{2}\mathbf{y}\mathbf{+}\mathbf{7}\mathbf{>}\mathbf{11}$

Short answer

Solution of the inequality is $y>2$.

Step-by-step solution

Step 1. Solve the inequality

$2y+7>11$

Subtract 7 from both the sides.

$\begin{array}{c}2y+7-7>11-7\\ 2y>4\end{array}$

Divide both sides by 2.

$\begin{array}{c}y>\frac{4}{2}\\ y>2\end{array}$

Step 2. Graph the inequality

The solution of the inequality is $y>2$.

That means, all values $y>2$ 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, $y>2$ and substitute in the original inequality and observe the result.

Take $y=4$.

Then,

$\begin{array}{c}2\times 4+7>11\\ 8+7>11\\ 15>11\end{array}$

The result$15>11$ is true. So, the solution$y>2$ is correct.