The inequality given is:

\[
17 < 3b + 5 < 29
\]

We will solve this compound inequality step by step.

### Step 1: Isolate the middle term

First, subtract 5 from all parts of the inequality to eliminate the constant on the middle term:

\[
17 - 5 < 3b + 5 - 5 < 29 - 5
\]

This simplifies to:

\[
12 < 3b < 24
\]

### Step 2: Solve for \( b \)

Now, divide all parts of the inequality by 3:

\[
\frac{12}{3} < \frac{3b}{3} < \frac{24}{3}
\]

This simplifies to:

\[
4 < b < 8
\]

### Final Solution:

The solution to the inequality is:

\[
4 < b < 8
\]

This means that \( b \) must be greater than 4 and less than 8.

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. How do you solve inequalities involving absolute values?
2. What is the difference between solving linear equations and inequalities?
3. How do compound inequalities differ from regular inequalities?
4. Can inequalities be solved graphically? How?
5. How do inequalities change when multiplied or divided by a negative number?

**Tip:** When dividing or multiplying inequalities by a negative number, always remember to reverse the inequality signs.

Learn how to solve the compound inequality 17 < 3b + 5 < 29 with a detailed step-by-step solution. This problem covers key algebraic concepts such as isolating the variable, applying inequality properties, and simplifying. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation