Question

Solve the inequality: 4z + 1 < 0. When is this inequality true?

A. Whenever z is greater than –5
B. One-quarter of z is less than 1
C. One-quarter of z is greater than 1
D. z is less than –1/4

Answer 1

The inequality 4z + 1 < 0 is solved by subtracting 1 from both sides to get 4z < -1, then dividing by 4, resulting in z < -1/4. The correct answer is D. Z is less than -1/4.

Step-by-step explanation:

To solve the inequality 4z + 1 < 0, we need to isolate the variable z on one side:

1. Subtract 1 from both sides of the inequality: 4z + 1 - 1 < 0 - 1, which simplifies to 4z < -1.
2. Divide both sides by 4 to solve for z: 4z/4 < -1/4, which simplifies to z < -1/4.

The inequality is true when z is less than -1/4. Looking at the options, D. z is less than -1/4 is the correct answer.