Choose the correct solution and graph for the inequality.
2x - 2 < -12 or 2x + 3 > 7
First, let's solve the first inequality:
2x - 2 < -12
Adding 2 to both sides:
2x - 2 + 2 < -12 + 2
2x < -10
Dividing both sides by 2:
2x/2 < -10/2
x < -5
Now, let's solve the second inequality:
2x + 3 > 7
Subtracting 3 from both sides:
2x + 3 - 3 > 7 -3
2x > 4
Dividing both sides by 2:
2x/2 > 4/2
x > 2
Therefore, the solution to the inequality is x < -5 or x > 2.
Now, let's graph the solution on a number line. Mark -5 and 2 with open circles (indicating that these values are not included in the solution), and shade the region between these two points to show that any value less than -5 or greater than 2 is a solution.
-----(-5)------(2)-----