Question

How do you solve `3x - 5> - 2`?

Answer 1

`x > 1`

Explanation:

Treat an inequality in the same way as an equation, unless you mulltiply or divide by a negative number, in which case the inequality sign changes around.

`3x -5 > -2`

`3x > -2 +5" "larr` isolate the x-term

`3x >3`

`x >1" "larr` isolate x

Answer 2

We do the same operations to both sides of the inequality to find that

`x>1`

Explanation:

You solve an inequality using the same methods as a simple equality - by adding, subtracting, multiplying and dividing both sides with the same quantities, but with one minor exception. If you multiply (or divide) both sides by a negative quantity, it changes the direction of the inequality, i.e. `> -> <` and vice versa, `< -> >`.

Lets start by adding `5` to both sides of our inequality:

`3x-5+5> -2+5`

which gives

`3x > 3`

Now we can divide both sides by `3` (which is positive, so it leaves the direction of the inequality the same):

`(3x)/3 > 3/3`

which simplifies to

`x>1`