27≤−2x+7or

Question

13>−2x+7

Answer 1

To solve the inequalities, we need to isolate the variable x.

For the first inequality, 27 ≤ -2x + 7:

Subtracting 7 from both sides:
27 - 7 ≤ -2x
20 ≤ -2x

Dividing both sides by -2 (and reversing the inequality because we're dividing by a negative number):
20/(-2) ≥ x
-10 ≥ x

So the solution to the first inequality is x ≤ -10.

For the second inequality, 13 > -2x + 7:

Subtracting 7 from both sides:
13 - 7 > -2x
6 > -2x

Dividing both sides by -2 (and reversing the inequality because we're dividing by a negative number):
6/(-2) < x
-3 < x

So the solution to the second inequality is x > -3.

Now, combining the solutions for both inequalities:

The first inequality gives us x ≤ -10, and the second inequality gives us x > -3.

Considering both conditions, the solution is:
x > -3 and x ≤ -10.