Q43. - Algebra 2

Question

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

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

Step-by-Step Solution

Answer

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

Solution on number line is 

Step 1 - 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 $a<-b\text{ or }a>b$

Step 3 - Simplify 2 n - 7 &#8804; 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,

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

Step 3 - Graph the solution set

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