To solve the inequality \( 3w + 7 < 9w - 3 \), we can follow these steps:

### Step 1: Get all terms involving \( w \) on one side
Subtract \( 3w \) from both sides:

\[
7 < 9w - 3w - 3
\]

Simplifying the right side:

\[
7 < 6w - 3
\]

### Step 2: Isolate the \( w \)-term
Add 3 to both sides:

\[
7 + 3 < 6w
\]

Simplifying:

\[
10 < 6w
\]

### Step 3: Solve for \( w \)
Divide both sides by 6:

\[
\frac{10}{6} < w
\]

Simplify the fraction:

\[
\frac{5}{3} < w
\]

or equivalently:

\[
w > \frac{5}{3}
\]

Thus, the solution to the inequality is:

\[
w > \frac{5}{3}
\]

### Do you have any questions or would you like more details?

Here are 5 related questions:
1. How do you solve a compound inequality?
2. What happens if you multiply or divide by a negative number in an inequality?
3. How do you graph the solution \( w > \frac{5}{3} \) on a number line?
4. Can you explain the difference between solving an equation and solving an inequality?
5. How can inequalities be used to model real-world situations?

**Tip:** When solving inequalities, always remember that multiplying or dividing by a negative number reverses the inequality sign.

Learn how to solve the linear inequality 3w + 7 < 9w - 3 with a detailed step-by-step solution. This problem covers key algebraic concepts, including inequality manipulation and solving for a variable. Suitable for students in Grades 7-9.

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