Question

Use the inequality 18 < -3(4x - 2) Solve the inequality for x. Show your work.

Answer 1

Answer:

x > -1

Step-by-step explanation:

Simplify the inequality using the distributive property (multiply the term outside the bracket with each number inside the bracket). Then, isolate 'x' by performing the reverse operations for every number that's on the same side as 'x'. (Reverse operations 'cancel out' a number.)

18 < -3(4x - 2)           Expand this to simplify

18 < (-3)(4x) - (-3)(2)             Multiply -3 with 4x and -2

18 < -12x + 6               Start isolating 'x'

18 - 6 < -12x + 6 - 6                 Subtract 6 from both sides

18 - 6 < -12x                  '+ 6' is cancelled out on the right side

12 < -12x                    Subtracted 6 from 18 on the left side

12/-12 < -12x/-12                    Divide both sides by -12

12/-12 < x                    'x' is isolated. Simplify left side

-1 < x                    Answer

x > -1             Standard formatting puts variable on the left side