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Solve the inequality: 2(4x – 3) ≥ 2-3(3x) + 5x?

A) x > 0.5
B) x > 2
C) (-[infinity], 0.5]
D) (-[infinity], 2]

1 Answer

3 votes

Final answer:

To solve the inequality, simplify both sides and combine like terms. Then isolate the x term by adding and subtracting constants. Finally, solve for x by dividing both sides by the coefficient of x.

Step-by-step explanation:

To solve the inequality, we can simplify both sides of the inequality first. Distribute the 2 to the terms inside the parentheses and simplify the right side of the inequality. This gives us 8x - 6 ≥ 2 - 9x + 5x. Combining like terms, we have 8x - 6 ≥ 2 - 4x. Next, we can add 4x to both sides to eliminate the x term on the right side, giving us 12x - 6 ≥ 2. Finally, we can add 6 to both sides to isolate the x term, resulting in 12x ≥ 8.

To solve for x, we divide both sides by 12, giving us x ≥ 8/12, which simplifies to x ≥ 2/3. Thus, the solution to the inequality is x ≥ 2/3.