Question

Solve each inequality.

$a+2>-2\text{or}a-8<1$

Short answer

Solution of inequality is $a>-4\text{or}a<9$

Step-by-step solution

- Write properties of inequality

Properties of inequalities are written in following table:

- Simplify a+2>-2

To simplify given inequality, use subtraction property of inequalities. Subtract by same number does not change the sign of inequality as shown below

$\begin{array}{c}a+2-2>-2-2\\ a>-4\end{array}$

- Simplify a-8<1

To simplify given inequality, use addition property of inequalities. Add by same number does not change the sign of inequality as shown below

$\begin{array}{c}a-8+8<1+8\\ a<9\end{array}$

Thus, solution is $a>-4\text{or}a<9$