Question

How do you solve `a-2<3a+2(a+3)`?

Answer 1

`a > -2`

Explanation:

Given:
`color(white)("XXX")a-2 < 2a+2(a+3)`

Simplify the right side:
`color(white)("XXX")a-2 < 3a +2a+6`

`color(white)("XXX")a-2 < 5a+6`

Subtract `(a+6)` from both sides
`color(white)("XXX")-8 < 4a`

Divide both sides by `4`
`color(white)("XXX")-2 < acolor(white)("XX")orcolor(white)("XX")a > -2`

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Remember:
When working with inequalities you can:
`color(white)("XXX")`add or subtract the same amount to both sides; and
`color(white)("XXX")`multiply or divide both sides by the same positive amount.
without changing the direction of the inequality sign.

If you multiply or divide both sides by an negative amount:
`color(white)("XXX")`the inequality sign must be reversed.