Final answer:
To solve the inequality 2 < -2x + 6 or -18 > -2x + 6, subtract 6 from both sides of each inequality to isolate -2x. Divide by -2 and reverse the inequality sign to find the solution x > 12.
Step-by-step explanation:
To solve the inequality 2 < -2x + 6 or -18 > -2x + 6, we need to solve for x.
For the first inequality, subtract 6 from both sides to isolate -2x. We get -4 < -2x. Divide both sides by -2 and reverse the inequality sign since we're dividing by a negative number, resulting in x > 2.
For the second inequality, subtract 6 from both sides to isolate -2x. We get -24 > -2x. Divide both sides by -2 and reverse the inequality sign, resulting in x > 12.
The solution to the original inequality is x > 12.