Question

Choose the correct solution and graph for the inequality.
2x-2-12 or 2x + 3 > 7

Answer 1

To solve the inequality 2x - 2 < -12, we will follow these steps:

Step 1: Add 2 to both sides of the inequality:
2x - 2 + 2 < -12 + 2
2x < -10

Step 2: Divide both sides of the inequality by 2 (since the coefficient of x is 2):
2x/2 < -10/2
x < -5

Therefore, the solution to the inequality 2x - 2 < -12 is x < -5.

To graph the solution on a number line, draw an open circle at -5 and shade the line to the left of -5.

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

Step 1: Subtract 3 from both sides of the inequality:
2x + 3 - 3 > 7 - 3
2x > 4

Step 2: Divide both sides of the inequality by 2 (since the coefficient of x is 2):
2x/2 > 4/2
x > 2

Therefore, the solution to the inequality 2x + 3 > 7 is x > 2.

To graph the solution on a number line, draw an open circle at 2 and shade the line to the right of 2.

To summarize, the correct solution is x < -5 OR x > 2.
The graph for this inequality would have an open circle at -5, a shaded line to the left of -5, an open circle at 2, and a shaded line to the right of 2.