Solving rational inequality solve for x-1 over 3+3 greater than 0 

To solve the rational inequality:

\[
\frac{x - 1}{3} + 3 > 0
\]

### Step 1: Simplify the inequality
Start by isolating the fraction by subtracting 3 from both sides:

\[
\frac{x - 1}{3} > -3
\]

### Step 2: Eliminate the denominator
Multiply both sides of the inequality by 3 to get rid of the denominator:

\[
x - 1 > -9
\]

### Step 3: Solve for \(x\)
Add 1 to both sides:

\[
x > -8
\]

### Final Answer:
The solution to the inequality is:

\[
x > -8
\]

This means that \(x\) must be greater than \(-8\).

Would you like further details or clarification? Here are some related questions:

1. How would the inequality change if the numerator was a quadratic expression?
2. What if the sign of the inequality was less than \(0\) instead of greater than \(0\)?
3. How can rational inequalities with variable denominators be solved?
4. How do you solve rational inequalities involving absolute values?
5. How do you solve compound inequalities?

**Tip**: Always be cautious about dividing or multiplying both sides of an inequality by a negative number—it reverses the inequality sign!

Solving rational inequality solve for (x - 1) / 3 + 3 greater than 0

Learn how to solve the rational inequality (x - 1) / 3 + 3 > 0 with this step-by-step guide. This solution explains how to simplify inequalities, eliminate denominators, and solve linear expressions. Suitable for students in Grades 8-10, focusing on key algebraic principles.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation