Solve for 
\[q\].
Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
\[22q+73 > 52q + 63\]

We are given the inequality:

\[
22q + 73 > 52q + 63
\]

### Step 1: Move all terms involving \(q\) to one side
Subtract \(22q\) from both sides to start isolating \(q\):

\[
73 > 52q - 22q + 63
\]

This simplifies to:

\[
73 > 30q + 63
\]

### Step 2: Move the constant terms to the other side
Subtract 63 from both sides:

\[
73 - 63 > 30q
\]

This simplifies to:

\[
10 > 30q
\]

### Step 3: Solve for \(q\)
Divide both sides by 30 to isolate \(q\):

\[
\frac{10}{30} > q
\]

Simplifying the fraction:

\[
\frac{1}{3} > q
\]

or equivalently,

\[
q < \frac{1}{3}
\]

Thus, the solution is:

\[
q < \frac{1}{3}
\]

Would you like a detailed explanation of any step? Here are some related questions you might explore:

1. How do you solve an inequality with negative numbers?
2. What happens if you multiply or divide both sides of an inequality by a negative number?
3. How do inequalities behave when dealing with absolute values?
4. Can you graph the solution of this inequality on a number line?
5. How does solving a system of inequalities differ from solving a single inequality?

**Tip:** Always remember that when you multiply or divide both sides of an inequality by a negative number, the inequality sign flips!

Solve for \[q\]. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. \[22q+73 > 52q + 63\]

Learn how to solve the inequality 22q + 73 > 52q + 63 with a detailed step-by-step solution. This problem involves algebraic manipulation of inequalities and is suitable for students in Grades 8-10. Understand how to isolate variables and reduce fractions.

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