Question

Solve the compound inequality 3 ≤ 4x + 9 < 25 expressing the solution set in interval notation.

A. (-6, 16]
B. (-4, 16)
C. [-6, 16)
D. [-4, 16]

Answer 1

The compound inequality 3 ≤ 4x + 9 < 25 can be solved in steps, resulting in the interval [-1.5, 4) as the solution. However, none of the provided answer choices match this correct solution.the correct answer is option c) [-6, 16)

Step-by-step explanation:

To solve the compound inequality 3 ≤ 4x + 9 < 25, we will solve each part of the inequality separately and then find the intersection of the two solutions.

First, let's solve the left part of the inequality:

1. 3 ≤ 4x + 9
2. Subtract 9 from both sides: -6 ≤ 4x
3. Divide by 4 on both sides: -1.5 ≤ x

Now let's solve the right part of the inequality:

1. 4x + 9 < 25
2. Subtract 9 from both sides: 4x < 16
3. Divide by 4 on both sides: x < 4

Combining both inequalities we get:

-1.5 ≤ x < 4

Expressed in interval notation, the solution is [ -1.5, 4 ).

However, none of the multiple choice options provided by the student match the correct solution. There is likely an error in the question or the provided options.