https://file.aiquickdraw.com/mathbot/file/1726630444661v9c2p1xj.jpg

The inequality in the image is:

\[
-4|2x - 3| \geq -20
\]

### Step-by-step solution:

1. **Divide both sides by -4** (remember that dividing an inequality by a negative number flips the inequality sign):

\[
|2x - 3| \leq 5
\]

2. **Solve the absolute value inequality**: 

This inequality \(|2x - 3| \leq 5\) can be rewritten as:

\[
-5 \leq 2x - 3 \leq 5
\]

3. **Solve for \(x\)** by adding 3 to all parts:

\[
-5 + 3 \leq 2x \leq 5 + 3
\]

\[
-2 \leq 2x \leq 8
\]

4. **Divide by 2**:

\[
-1 \leq x \leq 4
\]

### Final solution:
The solution set is \([-1, 4]\).

The correct answer would be option **B**, and the solution in interval notation is:

\[
[-1, 4]
\]

Would you like further details or have any questions?

Here are five related questions to deepen your understanding:

1. How do you solve absolute value inequalities with a "greater than" symbol?
2. What changes in the solution if the inequality sign had been strict (i.e., \(<\) instead of \(\leq\))?
3. How do you graph the solution set on a number line?
4. How does dividing or multiplying by a negative number affect inequality signs?
5. Can absolute value inequalities have no solutions? If so, under what conditions?

**Tip**: When solving inequalities, always remember to flip the inequality sign when multiplying or dividing by a negative number!

Solve the inequality. Graph the solution set. -4|2x - 3| ≥ -20

Learn how to solve the absolute value inequality -4|2x - 3| ≥ -20 with step-by-step guidance. This problem covers key algebraic concepts, including solving absolute value inequalities and understanding how the inequality sign changes when dividing by a negative number. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation