2r - 5/3r > negative1/3 Enter the simplified inequality in the box.
Use the properties of inequality to isolate the variable on one side.

Let's solve the inequality step by step.

### Given inequality:
\[
2r - \frac{5}{3}r > -\frac{1}{3}
\]

### Step 1: Combine like terms.
Combine the terms involving \(r\):
\[
\left(2 - \frac{5}{3}\right)r > -\frac{1}{3}
\]

To subtract the fractions, find a common denominator:
\[
2 = \frac{6}{3}
\]
So,
\[
\frac{6}{3} - \frac{5}{3} = \frac{1}{3}
\]
Thus, the inequality becomes:
\[
\frac{1}{3}r > -\frac{1}{3}
\]

### Step 2: Isolate the variable \(r\).
Multiply both sides of the inequality by 3 to get rid of the fraction:
\[
r > -1
\]

### Final Answer:
\[
r > -1
\]

Do you want more details or have any questions? Here are some related questions:

1. How do you solve inequalities with multiple variables?
2. How does multiplying or dividing by a negative number affect an inequality?
3. Can you graph the solution of \(r > -1\) on a number line?
4. How would you solve the inequality if it had an "equal to" component?
5. What are the properties of inequalities that are essential in solving them?

**Tip:** Always remember to reverse the inequality sign when multiplying or dividing both sides by a negative number.

Learn how to solve the inequality 2r - (5/3)r > -1/3 with a detailed step-by-step solution. This problem involves solving linear inequalities and understanding fraction manipulation. Suitable for Grades 9-12 students studying algebra and inequalities.

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