Question

Solve for x. the absolute value of 3x-5 > 19

Answer 1

• x < -14/3

or

• x > 8

Explanation:

To solve the inequality |3x-5| > 19, we need to consider two cases:

→ Case 1: 3x-5 > 19

In this case, we isolate x by adding 5 to both sides of the inequality:

• 3x > 24

Next, divide both sides of the inequality by 3 to solve for x:

• x > 8

→ Case 2: -(3x-5) > 19

In this case, we isolate x by multiplying both sides of the inequality by -1 and changing the direction of the inequality:

• 3x-5 < -19

Next, add 5 to both sides of the inequality:

• 3x < -14

Finally, divide both sides of the inequality by 3 to solve for x:

• x < -14/3

So, the solution to the inequality |3x-5| > 19 is x < -14/3 or x > 8.