Question

How do you solve the inequality: `-5(13x + 3) < - 2(13x - 3)`?

Answer 1

`x in (-7/13, + oo)`

Explanation:

Start by dividing both sides of the inequality by `(-1)` - do not forget to change the sign of the inequality when you do this

`(-5(13x + 3))/((-1)) > (-2(13x - 3))/((-1))`

`5(13x + 3) > 2(13x - 3)`

Next, use the distributive property of multiplication to expand the two parantheses

`5 * 13x + 5 * 3 > 2 * 13x + 2 * (-3)`

`65x + 15 > 26x - 6`

Rearrange to get the `x`-term on one side of the inequality

`65x - 26x > -6 - 15`

`39x > - 21 implies x > -21/39 = -7/13`

This means that your inequality will be true for any value of `x` that is greater than `-7/13`. The solution set for this inequality will be `x in (-7/13, + oo)`.