3(4x-2)<2(5x-8) Solve and Check

Question

Here is a question I have, I originally got -11 but when I checked it did not come out right not sure what I did wrong though.

Answer 1

The inequality is 3(4x-2) < 2(5x-8).

Apply distributive property: a (b - c) = ab - ac.

12x - 6 < 10x - 16

Subtract 10x from each side.

12x - 6 -10x < 10x - 16 -10x

2x - 6 < -16

Add 6 to each side.

2x - 6 + 6 < -16 + 6

2x < -10

Divide each side by 2.

2x/2 < -10/2

x < -5.

Check:-

To check the solution, the value of x = -6 (since -6 < -5) in the original inequality.

3(4(-6)-2) < 2(5(-6)-8)

3(-24 -2) < 2(-30 -8)

3(-26) < 2(-38)

-78 < -76

The above statement is true, so the value of {x| x < -5} is a solution of the original inequality.