Choose the correct solution and graph for the inequality
2x-2<-12 or 2x+3>7
To solve the inequality 2x - 2 < -12, we can add 2 to both sides of the inequality:
2x - 2 + 2 < -12 + 2
2x < -10
Next, we isolate x by dividing both sides of the inequality by 2:
2x/2 < -10/2
x < -5
To solve the inequality 2x + 3 > 7, we can subtract 3 from both sides of the inequality:
2x + 3 - 3 > 7 - 3
2x > 4
Next, we isolate x by dividing both sides of the inequality by 2:
2x/2 > 4/2
x > 2
Therefore, the correct solution is: x < -5 or x > 2.
To graph this solution on a number line, we can plot an open circle at -5 (since x is less than -5) and shade to the left, indicating all the values less than -5. Then, we can plot an open circle at 2 (since x is greater than 2) and shade to the right, indicating all the values greater than 2.
The graph on the number line would look like this:
--------o------o--------
-5 2
Here, the open circles at -5 and 2 indicate that these values are not included in the solution, while the shaded regions indicate all the values that satisfy the inequality.