Question

How do you solve the inequality `2(x-3) <4(x+1/2)`?

Answer 1

Simplify the the expression on each side; add and subtract to isolate `x`; then reverse the inequality to get
`color(white)("XXX")x > -4`

Explanation:

`2(x-3) < 4(x+1/2)`

Expand the expression on each side:
`2x-6 < 4x + 2`

Subtract `(2x+2)` from both sides
(you can always subtract the same amount from both sides of an inequality with out effecting the validity or orientation of the inequality)
`-8 < 2x`

Divide both sides by `2`
(you can always multiply or divide by any amount `>0` without effecting the validity or orientation of the inequality)
`-4 < x`

Reversal of inequality (doesn't really change it but makes it look more standard)
`x > -1`