Solve and graph the solution set.
33xminus−22greater than>nothingxplus+22
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Part 1
Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The solution set is enter your response here.
​(Simplify your answer. Type your answer in interval​ notation.)
B.
There is no solution.

The inequality you're solving is:

\[
33x - 22 > x + 22
\]

Let's solve this step by step.

### Step 1: Subtract \(x\) from both sides.
\[
33x - x - 22 > 22
\]
\[
32x - 22 > 22
\]

### Step 2: Add 22 to both sides.
\[
32x - 22 + 22 > 22 + 22
\]
\[
32x > 44
\]

### Step 3: Divide both sides by 32.
\[
x > \frac{44}{32}
\]
\[
x > \frac{11}{8}
\]

### Final Answer:
The solution set is \( x > \frac{11}{8} \).

In interval notation, the solution is:
\[
\boxed{ \left( \frac{11}{8}, \infty \right) }
\]

### Graph of the solution:
- The graph will show a number line with an open circle at \( x = \frac{11}{8} \), and the line will extend to the right, representing all numbers greater than \( \frac{11}{8} \).

Would you like a visual graph of this solution?

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Here are 5 related questions for practice:
1. Solve \( 5x - 3 > 2x + 7 \).
2. Solve \( 7x + 4 < 2x - 6 \).
3. Solve and graph \( 10x - 4 \geq 6x + 8 \).
4. Solve \( 3x - 2x \leq 4 + 5x - 6 \).
5. What does interval notation mean for \( (-\infty, 3) \)?

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

Solve and graph the solution set: 33x - 22 > x + 22. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Simplify your answer. Type your answer in interval notation.) B. There is no solution.

This solution demonstrates how to solve and graph the inequality 33x - 22 > x + 22. It involves core algebraic concepts such as inequality manipulation and the properties of linear equations. Step-by-step instructions help simplify the inequality to find x > 11/8 and represent it in interval notation.

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