Question

−7x−50≤−1 AND−6x+70>−2

Answer 1

`-7\geq x<12` and
`[-7,12)` in interval notation.

Explanation:

We have been given a compound inequality
`-7x-50\leq -1\text{ and }-6x+70>-2`. We are supposed to find the solution of our given inequality.

First of all, we will solve both inequalities separately, then we will combine both solution merging overlapping intervals.

`-7x-50\leq -1`

`-7x-50+50\leq -1+50`

`-7x\leq 49`

Dividing by negative number, flip the inequality sign:

`(-7x)/(-7)\geq (49)/(-7)`

`x\geq -7`

`-6x+70>-2`

`-6x+70-70>-2-70`

`-6x>-72`

Dividing by negative number, flip the inequality sign:

`(-6x)/(-6)<(-72)/(-6)`

`x<12`

Upon merging both intervals, we will get:

`-7\geq x<12`

Therefore, the solution for our given inequality would be
`-7\geq x<12` and
`[-7,12)` in interval notation.