Question

How do you solve the inequality `7a<12a+10`?

Answer 1

`-2 < a`

Explanation:

Treat the inequality as an equals sign and solve normally. Be careful when dividing by a negative number but apart from that you're good to go!

Answer 2

`a> -12/5`

`a > -2 1/2`

Explanation:

`7a < 12a +10`

Treat an inequality in the same way as an equation. However if you multiply or divide by a negative number, the inequality sign will change around.

Therefore, try to keep the variable terms positive to avoid this.

Transposing the inequality can lead to:

`7a-12a < 12 " or "-12 < 12a -7a`

`color(red)(-5a < )12" or " color(blue)(-12 <5a)larr` this one is preferable
`color(white)(x....x)darr`
`color(red)((-5a)/(-5) >) 12/(-5)" or "color(blue)(-12 <5a)`

`color(red)(a) > -12/5" or "color(blue)(-12/5 < (5a)/5)`

`color(blue)(-12/5 < a)" "` can also be written as `a > -12/5`

`a > -2 1/2`