Let's solve the inequality \(-\frac{5}{2}(3x + 4) < 6 - 3x\).

### Step 1: Distribute \(-\frac{5}{2}\) on the left side.
\[
-\frac{5}{2} \cdot 3x - \frac{5}{2} \cdot 4 < 6 - 3x
\]
\[
-\frac{15}{2}x - 10 < 6 - 3x
\]

### Step 2: Add \(3x\) to both sides to move all terms involving \(x\) to one side.
\[
-\frac{15}{2}x + 3x - 10 < 6
\]

### Step 3: Combine like terms.
To combine \(-\frac{15}{2}x\) and \(3x\), note that \(3x = \frac{6}{2}x\):
\[
\left(-\frac{15}{2} + \frac{6}{2}\right)x - 10 < 6
\]
\[
-\frac{9}{2}x - 10 < 6
\]

### Step 4: Add 10 to both sides to isolate the term involving \(x\).
\[
-\frac{9}{2}x < 16
\]

### Step 5: Multiply both sides by \(-\frac{2}{9}\) to solve for \(x\). Remember to reverse the inequality sign because you're multiplying by a negative number.
\[
x > \frac{16 \times (-2)}{9}
\]
\[
x > -\frac{32}{9}
\]

### Final Answer:
\[
x > -\frac{32}{9}
\]

This is the solution to the inequality.

Would you like further details or have any questions?

Here are 5 related questions you could explore:
1. How do you solve inequalities with fractions on both sides?
2. What happens to an inequality when you multiply or divide by a negative number?
3. Can you graph the solution to the inequality \(x > -\frac{32}{9}\)?
4. How do you handle inequalities that involve distributing a negative fraction?
5. What are the steps to solving a compound inequality?

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

Learn how to solve the inequality 5/2(3x + 4) < 6 - 3x using key algebraic concepts such as distribution, combining like terms, and handling inequalities with fractions. Step-by-step instructions guide you through this problem suitable for 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