Q48. - Algebra 2

Question

Solve each inequality. Graph the solution set on a number line.

48. $\left|\mathbf{x}\right|\mathbf{+}\mathbf{1}>\mathbf{12}$

Step-by-Step Solution

Answer

Solution set of inequality is $\left\{\mathbf{x}\mathbf{|}\mathbf{x}>\mathbf{11}\mathbf{orx}<\mathbf{-}\mathbf{11}\right\}$.

Solution set on number line is 

Step 1 - Write properties of inequality.

Properties of inequalities are written in following table:

Step 2 - Solve x + 1 &#62; 12 .

Subtract 1 from each side and simplify.

$\begin{array}{c}\left|x\right|+1-1>12-1\\ \left|x\right|>11\end{array}$

Step 3 &ndash; Description of step.

$\left|x\right|>11$ is equivalent to $x>11$ or $x<-11$.

 

Thus, solution is $x>11$ or $x<-11$.

Step 4 &ndash; Graph the solution set.

As solution set of the inequality is all real numbers greater than 11 or less than $-11$.

The solution set is, $\left\{x|x>11\text{ or }x<-11\right\}$.

Open circles on $-11$ and 11 shows this point is excluded in the solution set.