Question

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

43. $\left|2n-7\right|\le 0$

Short answer

Given inequality has solution $n=\frac{7}{2}$

Solution on 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 2n-7≤0

From definition of absolute value, it is the distance of a point from 0, so it is always greater than or equal to 0. But in given expression absolute value is less than or equal to 0 so it has only one solution point when 2n-7=0

Simplify this expression to get,

$\begin{array}{c}2n-7=0\\ 2n=7\\ n=\frac{7}{2}\end{array}$

- Graph the solution set

As given expression has only one solution point, so it is represented on number line by marking that point