Question

−7x−50≤−1 AND−6x+70>−2

Answer 1

Answer:

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

Step-by-step 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:

$\frac{-7x}{-7}\geq \frac{49}{-7}$

$x\geq -7$

$-6x+70>-2$

$-6x+70-70>-2-70$

$-6x>-72$

Dividing by negative number, flip the inequality sign:

$\frac{-6x}{-6}<\frac{-72}{-6}$

$x<12$

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.