Question

What is the solution set for
22 ≥ 4m - 2 or 5 - 3m ≤ -13

Answer 1

So the solution set for the given system of inequalities is all real numbers.

Explanation:

We have two inequalities:

22 ≥ 4m - 2 or 5 - 3m ≤ -13

We can solve each inequality separately and then take the union of the solution sets.

Solving the first inequality:

22 ≥ 4m - 2

Add 2 to both sides:

24 ≥ 4m

Divide both sides by 4:

6 ≥ m

So the solution set for the first inequality is m ≤ 6.

Solving the second inequality:

5 - 3m ≤ -13

Add 3m to both sides:

5 ≤ 3m - 13

Add 13 to both sides:

18 ≤ 3m

Divide both sides by 3:

6 ≤ m

So the solution set for the second inequality is m ≥ 6.

Taking the union of the solution sets, we get:

m ≤ 6 or m ≥ 6

This can be simplified to:

m ∈ (-∞, ∞)

So the solution set for the given system of inequalities is all real numbers.