https://file.aiquickdraw.com/mathbot/file/1725427017451wj2aqrse.jpg

Let's solve the inequality given in the image:

\[
\frac{3}{5}(x + 2) > 9 - 3(x - 1)
\]

### Step 1: Distribute the terms
First, we'll distribute the \(\frac{3}{5}\) on the left side and the \(-3\) on the right side:

\[
\frac{3}{5} \cdot x + \frac{3}{5} \cdot 2 > 9 - 3 \cdot x + 3
\]

This simplifies to:

\[
\frac{3x}{5} + \frac{6}{5} > 9 - 3x + 3
\]

### Step 2: Simplify the equation
Combine like terms on the right side:

\[
\frac{3x}{5} + \frac{6}{5} > 12 - 3x
\]

### Step 3: Eliminate the fraction
To eliminate the fraction, multiply every term by 5:

\[
5 \left(\frac{3x}{5} + \frac{6}{5}\right) > 5 \cdot (12 - 3x)
\]

This gives:

\[
3x + 6 > 60 - 15x
\]

### Step 4: Move terms involving \(x\) to one side
Add \(15x\) to both sides:

\[
3x + 15x + 6 > 60
\]

Simplify:

\[
18x + 6 > 60
\]

### Step 5: Solve for \(x\)
Subtract 6 from both sides:

\[
18x > 54
\]

Finally, divide by 18:

\[
x > 3
\]

### Solution Set
The solution set for the inequality is:

\[
x > 3
\]

This means that the inequality holds true for all \(x\) greater than 3.

Would you like more details or have any questions about this process? Here are some related questions:

1. What happens if \(x = 3\) is included in the solution set?
2. How would the solution change if the inequality were \(<\) instead of \(>\)?
3. Can you graph the solution set on a number line?
4. What if the coefficient on \(x\) were negative? How would that affect the inequality?
5. How do you solve similar inequalities involving absolute values?

**Tip:** Always check your final solution by substituting values back into the original inequality to ensure they satisfy the condition.

Find the solution set for the inequality: 3/5(x + 2) > 9 - 3(x - 1)

Learn how to solve the inequality 3/5(x + 2) > 9 - 3(x - 1) with a step-by-step solution. This problem covers key algebraic concepts including inequalities, distribution, and clearing fractions. Ideal for students in Grades 9-11.

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