Question

M - 7 ≥ -3 or -2m + 1 ≥ 11

Answer 1

To solve this compound inequality, let's work on each inequality separately.

For the first inequality, m - 7 ≥ -3, we can solve it as follows:

m - 7 ≥ -3

Adding 7 to both sides:

m - 7 + 7 ≥ -3 + 7

Simplifying:

m ≥ 4

So the solution to the first inequality is m ≥ 4.

Now let's move on to the second inequality, -2m + 1 ≥ 11:

-2m + 1 ≥ 11

Subtracting 1 from both sides:

-2m + 1 - 1 ≥ 11 - 1

Simplifying:

-2m ≥ 10

Dividing both sides by -2 (remember to reverse the inequality when dividing by a negative number):

m ≤ -5

So the solution to the second inequality is m ≤ -5.

Therefore, the combined solution for the compound inequality is m ≤ -5 or m ≥ 4.