Question

How do you solve the inequality `2(x - 4)< 8(x + 1/2)`?

Answer 1

`x > -4/3`

Explanation:

Given
`color(white)("XXX")2(x-4) < 8(x+1/2)`

Simplify both sides
`color(white)("XXX")2x-4 < 8x + 4`

Add 4 to both sides
`color(white)("XXX")2x < 8x +8`

Subtract `8x` from both sides
`color(white)("XXX")-6x < 8`

Divide both sides by `(-6)`
Remember that multiplying or dividing by a number less than zero requires that you reverse the inequality sign
`color(white)("XXX")x > -4/3`