Solve the inequality

Question

5|x−3|>15
(1 point)
Responses

x<0 or x>6
x<0 or x>6

0<x<6
0<x<6

x<−12 or x>18
x<−12 or x>18

x<−6 or x>0

Answer 1

To solve the inequality 5|x-3| > 15, we can start by dividing both sides of the inequality by 5:

|x-3| > 3.

Since the absolute value of a number is always greater than or equal to 0, we can rewrite the inequality as:

x-3 > 3 or -(x-3) > 3.

Simplifying each inequality:

x > 6 or -x + 3 > 3.

For the second inequality, we can subtract 3 from both sides:

-x > 0.

Multiplying both sides by -1 and flipping the inequality sign:

x < 0.

Therefore, the solution to the inequality is x > 6 or x < 0.