31≥−4x+7and

Question

−4x+7>−13

Answer 1

To solve these inequalities, we can treat them individually and then find their intersection.

31 ≥ -4x + 7

Subtracting 7 from both sides, we get:

24 ≥ -4x

Dividing both sides by -4 and flipping the inequality sign since we are dividing by a negative number gives us:

-6 ≤ x

Now let's solve the second inequality:

-4x + 7 > -13

Subtracting 7 from both sides:

-4x > -20

Dividing both sides by -4 and flipping the inequality sign gives us:

x < 5

Now let's find the intersection of the two inequalities:

Since -6 ≤ x and x < 5, the common range of values that satisfy both inequalities is:

-6 ≤ x < 5