Question

Solve each inequality. Then graph it on a number line.

$\mathbf{-}\mathbf{5}\mathbf{<}\mathit{a}\mathbf{+}\mathbf{2}$

Short answer

The solution of the given inequality $-5<a+2$is $\mathit{a}\mathbf{>}\mathbf{-}\mathbf{7}$.

The graph of the solution of the given inequality $-5<a+2$that is graph of $a>-7$is:

Step-by-step solution

Step 1. Write the subtraction property of inequalities.

The subtraction property of inequalities states that if the same number is subtracted from each side of a true inequality, the resulting inequality is also true that is:

(i) If $a>b$, then $a-c>b-c$.

(ii) If $a<b$, then $a-c<b-c$.

Step 2. Solve the given inequality.

The solution of the given inequality$-5<a+2$ is:

$\begin{array}{c}-5<a+2\\ -5-2<a+2-2\\ -7<a\\ a>-7\end{array}\left(\text{byusingsubtractionpropertyofinequality}\right)$

Therefore, the solution of the given inequality$-5<a+2$ is $a>-7$.

Step 3. Draw the graph of the inequality a>−7.

The graph of the solution of the given inequality$-5<a+2$ that is graph of$a>-7$ is:

It can be noticed that at $a=-7$, there is open circle because$-7$ is not included in the inequality $a>-7$.