2r-5/3r > -1/3 Enter the simplified inequality in the box.

To solve the inequality \( \frac{2r - 5}{3r} > -\frac{1}{3} \), follow these steps:

1. **Multiply both sides by \( 3r \)** to eliminate the denominator. Assuming \( r \) is not zero:
   \[
   3r \cdot \frac{2r - 5}{3r} > 3r \cdot \left(-\frac{1}{3}\right)
   \]
   Simplifies to:
   \[
   2r - 5 > -r
   \]

2. **Add \( r \) to both sides** to get:
   \[
   3r - 5 > 0
   \]

3. **Add 5 to both sides** to isolate the term with \( r \):
   \[
   3r > 5
   \]

4. **Divide by 3** to solve for \( r \):
   \[
   r > \frac{5}{3}
   \]

Thus, the simplified inequality is \( r > \frac{5}{3} \).

Would you like more details, or have any questions?

---

Here are 5 related questions for further practice:
1. Solve the inequality \( \frac{4r - 7}{2r} > \frac{1}{2} \).
2. What happens to the inequality sign when multiplying or dividing by a negative number?
3. Solve \( 2r - 5 < 3r + 7 \).
4. Simplify and solve \( \frac{3r + 2}{r - 1} < 1 \).
5. How do you solve \( \frac{r + 4}{2r - 1} \leq \frac{3}{2} \)?

**Tip:** Always remember to check if multiplying or dividing by a variable could change the inequality direction, especially if the sign of the variable is unknown.

Learn how to solve the inequality (2r - 5) / (3r) > -1/3 step-by-step with detailed explanations and practice questions. This problem involves solving algebraic inequalities and understanding how to manipulate fractions and variables. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation