Question

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

$\left|3k\right|<0$

Short answer

Given inequality has no solution

Solution set in number line is empty

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 3k<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 0 so it has no solution.

- Graph the solution set

As given expression has no solution set, so it cannot be represented on number line.

Thus, there is no solution on number line, so it is empty.