Question

Which absolute value inequality represents the given graph?

 

 

A.	|–3x| < 15
B.	|–3x| > 15
C.
D.

 

Answer 1

On the number line diagram, heavy arrow drawn from - 5 to left side and 5 to right side So, the numbers below -5 and above 5 are solutions to the inequality.

On the number line diagram a dot is shown at -5 and 5. So, the numbers -5 and 5 are included in the solution set.

So, the solution set is {x ≤ -5 or x ≥ 5}.

To write a open sentence, find the point that is same distance from points -5 and 5.

The distance from 0 to -5 is 5 units.

The distance from 0 to 5 is 5 units.

So, the midpoint is 0.

 

The distance between 0 and x is greater than or equal to 5 units.

So, the open sentence for the given graph is |x| ≥ 5.

Multiply each side by |-3| .

|-3||x| ≥ |-3|(5)

|-3x| ≥ 15.

So option C is correct.