2x-2<-12\ or\ 2x+3>7

Answer 1

To solve the inequalities, we'll solve each one separately.
Let's start with 2x - 2 < -12:

Adding 2 to both sides of the inequality, we have:
2x - 2 + 2 < -12 + 2
2x < -10

Now, let's divide both sides by 2:
(2x)/2 < -10/2
x < -5

So the solution to the first inequality is x < -5.

Now let's solve 2x + 3 > 7:

Subtracting 3 from both sides of the inequality, we have:
2x + 3 - 3 > 7 - 3
2x > 4

Now dividing both sides by 2:
(2x)/2 > 4/2
x > 2

So the solution to the second inequality is x > 2.

Therefore, the solution to the system of inequalities is x < -5 or x > 2.