Question

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

$\left|n\right|\le n$

Short answer

Solution of inequality is all non-negative real number.

Solution set in number line is

Step-by-step solution

- Definition of absolute value inequality

For real numbers $a\text{and}b$with b>0

Absolute value inequality is $\left|a\right|<b$ when $-b<a\text{and}a<b$, and

Absolute value inequality is $\left|a\right|>b$ when $a<-b\text{or}a>b$

- Simplify n≥n

For $\left|a\right|<b$, b is always greater than 0

So let n is a positive number

From definition of absolute value inequality, given expression is simplified to

$-n\le n\text{and}n\le n$

Since, $-n\le n$is true only when n is positive real number and $n\le n$ is true for all real number.

Solution is “Non-negative real number” and “All real number”

The solution of compound inequality containing and is the intersection of the solution set of the two inequalities.

So solution is non-negative real number.

- Graph the solution set

As solution is all non-negative real number, so all points on number line start from 0 to $\infty$ are solution of given inequality.