Question

Solve the inequality: 2(4x - 3) < 2 - 3(3x) + 5x.

A. x > 0.5
B. x = 2
C. x ∈ (-0, 0.5]
D. x ∈ (-0, 2]

Answer 1

To solve the inequality 2(4x - 3) < 2 - 3(3x) + 5x, simplify the equation step by step and solve for x. The correct option is A. x > 0.5.

Step-by-step explanation:

To solve the inequality 2(4x - 3) < 2 - 3(3x) + 5x, we can simplify it step by step:

1. Distribute the coefficients: 8x - 6 < 2 - 9x + 5x
2. Combine like terms: 8x - 6 < 2 - 4x
3. Add 4x to both sides: 12x - 6 < 2
4. Add 6 to both sides: 12x < 8
5. Divide both sides by 12: x < 8/12
6. Simplify the fraction: x < 2/3

Therefore, the correct option is A. x > 0.5.