You have the compound inequality:

\[
-10 \leq \frac{4 - 7x}{2} \leq 11
\]

### Step 1: Break the inequality into two parts.

1. \(-10 \leq \frac{4 - 7x}{2}\)
2. \(\frac{4 - 7x}{2} \leq 11\)

We'll solve each part separately.

### Step 2: Solve the first inequality \(-10 \leq \frac{4 - 7x}{2}\)

Multiply both sides by 2 to eliminate the denominator:

\[
-10 \times 2 \leq 4 - 7x \quad \Rightarrow \quad -20 \leq 4 - 7x
\]

Now subtract 4 from both sides:

\[
-20 - 4 \leq -7x \quad \Rightarrow \quad -24 \leq -7x
\]

Divide both sides by \(-7\), remembering to reverse the inequality since we are dividing by a negative number:

\[
\frac{-24}{-7} \geq x \quad \Rightarrow \quad \frac{24}{7} \geq x
\]

Thus, \(x \leq \frac{24}{7}\).

### Step 3: Solve the second inequality \(\frac{4 - 7x}{2} \leq 11\)

Again, multiply both sides by 2:

\[
4 - 7x \leq 11 \times 2 \quad \Rightarrow \quad 4 - 7x \leq 22
\]

Subtract 4 from both sides:

\[
-7x \leq 22 - 4 \quad \Rightarrow \quad -7x \leq 18
\]

Now, divide both sides by \(-7\), remembering to reverse the inequality:

\[
x \geq \frac{18}{-7} \quad \Rightarrow \quad x \geq -\frac{18}{7}
\]

### Step 4: Combine the results

The solution is:

\[
-\frac{18}{7} \leq x \leq \frac{24}{7}
\]

This is the solution to the compound inequality.

---

Do you need further details or have any questions?

Here are 5 related questions for practice:
1. Solve \( -5 \leq \frac{3x + 2}{4} \leq 6 \).
2. Solve \( 2 \leq \frac{5 - 2x}{3} \leq 8 \).
3. Solve \( -8 \leq \frac{6x - 9}{4} \leq 10 \).
4. Solve \( 0 \leq \frac{4x + 1}{5} \leq 7 \).
5. Solve \( -7 \leq \frac{2x + 3}{6} \leq 9 \).

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

Learn how to solve the compound inequality -10 ≤ (4 - 7x)/2 ≤ 11 with step-by-step instructions. This guide covers key algebraic concepts, including multiplying and dividing inequalities by negative numbers. Ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation