Question

What is the solution set for the inequality 3(1 - 2x) > 2(-2x + 4) + 3?

A. x < 1
B. x > 1
C. x < -1
D. x > -1

Answer 1

To solve the inequality 3(1 - 2x) > 2(-2x + 4) + 3, the steps involve distributing, simplifying, moving terms to one side, and dividing by a negative number, yielding x < -4. This solution does not match any of the options given.

Step-by-step explanation:

To solve the inequality 3(1 - 2x) > 2(-2x + 4) + 3, we must perform the following steps:

1. Distribute the numbers outside the parentheses: 3 - 6x > -4x + 8 + 3.
2. Simplify the inequality: 3 - 6x > -4x + 11.
3. Add 6x to both sides to get all x terms on one side and constant terms on the other: 3 > 2x + 11.
4. Subtract 11 from both sides: -8 > 2x.
5. Divide both sides by 2, and remember to reverse the inequality sign because we're dividing by a negative number: x < -4.

Therefore, the solution set is x < -4, which is not represented by any of the options given (A. x < 1, B. x > 1, C. x < -1, D. x > -1). There must be an error in the options provided as they do not match the solution.