Question

Write and solve an equality for three-fourths of a number added to four is at least twenty-four.

a) 3/4x + 4 = 24
b) 3/4x + 4 ≥ 24
c) 4x + 3/4 = 24
d) 3/4x + 4 ≤ 24

Answer 1

The correct inequality is 3/4x + 4 ≥ 24. After subtracting 4 and multiplying both sides by 4/3, the solution is that x must be at least 26.67.

Step-by-step explanation:

The student has asked to write and solve an inequality that represents three-fourths of a number added to four being at least twenty-four. The correct inequality for this description is option b) 3/4x + 4 ≥ 24. Now, let's solve this inequality step-by-step.

1. Subtract 4 from both sides of the inequality: 3/4x ≥ 20.
2. Multiply both sides by the reciprocal of 3/4, which is 4/3, to isolate x: x ≥ 20 * (4/3).
3. Simplify the right side: x ≥ 26.67. Thus, x must be greater than or equal to 26.67.