Question

How do you solve `1/3x + 2 >3` and `-3x > 12`?

Answer 1

`3 < x <4`

Explanation:

Treat inequalities the same as equations, except if you multiply or divide by a negative value, in which case the inequality sign changes around.

`1/3x+2 >3color(white)(xxxxxxxxxxxxxx)-3x >12`

`1/3x > 1" "larr xx 3color(white)(xxxxxxxxxxx) 12>3x" "larr div3`

`x > 3color(white)(xxxxxxxxxxxxxxxxxxxxxx)4 >x`

Combine the two inequalities,

`3 < x and x < 4`

`:. 3 < x <4`