Let's solve the inequality \( 1 + 4\left(-\frac{1}{2}x - \frac{1}{3}\right) < -5 - x \).

### Step 1: Distribute the 4
First, distribute the 4 across the terms inside the parentheses:
\[
1 + 4\left(-\frac{1}{2}x\right) + 4\left(-\frac{1}{3}\right) < -5 - x
\]
This simplifies to:
\[
1 - 2x - \frac{4}{3} < -5 - x
\]

### Step 2: Combine like terms on the left-hand side
Next, combine the constants on the left-hand side:
\[
1 - \frac{4}{3} - 2x < -5 - x
\]
\[
\frac{3}{3} - \frac{4}{3} - 2x < -5 - x
\]
\[
-\frac{1}{3} - 2x < -5 - x
\]

### Step 3: Add \(2x\) to both sides to simplify
Add \(2x\) to both sides to isolate the variable \(x\):
\[
-\frac{1}{3} < -5 + x
\]

### Step 4: Add 5 to both sides
Finally, add 5 to both sides to further isolate \(x\):
\[
-\frac{1}{3} + 5 < x
\]

### Step 5: Simplify
\[
\frac{15}{3} - \frac{1}{3} < x
\]
\[
\frac{14}{3} < x
\]
Or equivalently,
\[
x > \frac{14}{3}
\]

### Final Answer:
The solution to the inequality is:
\[
x > \frac{14}{3}
\]

Do you want details or have any questions?  
Here are 5 related questions:
1. How do you solve inequalities with fractions?
2. What happens when you multiply or divide both sides of an inequality by a negative number?
3. Can you explain how to combine like terms in inequalities?
4. How do you graph the solution \(x > \frac{14}{3}\) on a number line?
5. What is the difference between solving equations and solving inequalities?

**Tip:** Always remember that when you multiply or divide an inequality by a negative number, you must flip the inequality sign.

Learn how to solve the linear inequality 1 + 4(-1/2x - 1/3) < -5 - x with a detailed step-by-step solution. This problem covers key algebraic concepts such as the distributive property, combining like terms, and solving inequalities. Suitable 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