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3 months ago

−7x−50≤−1 AND−6x+70>−2

Mathematics

1 answer:

PIT_PIT [12.4K]3 months ago

7 0

Answer:

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

Step-by-step explanation:

A compound inequality $-7x-50\leq -1\text{ and }-6x+70>-2$ has been provided. Our task is to determine the solution for this inequality.

Initially, we will address each inequality independently, followed by merging the findings by combining the overlapping intervals.

$-7x-50\leq -1$

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

$-7x\leq 49$

By dividing with a negative number, it is necessary to reverse the inequality sign:

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

$x\geq -7$

$-6x+70>-2$

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

$-6x>-72$

Again, dividing by a negative requires flipping the inequality sign:

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

$x$

In combining both intervals, we will arrive at:

$-7\geq x$

Thus, the solution for the inequality provided is $-7\geq x$ and $[-7,12)$ in interval notation.

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