Solve the inequality. Graph the solution on the number line and then give the answer in interval notation. -2x + 9< 5

To solve the inequality \(-2x + 9 < 5\), follow these steps:

### Step 1: Isolate the variable
Subtract 9 from both sides of the inequality:

\[
-2x + 9 - 9 < 5 - 9
\]

This simplifies to:

\[
-2x < -4
\]

### Step 2: Solve for \(x\)
Divide both sides by \(-2\). Remember that when dividing or multiplying both sides of an inequality by a negative number, the inequality sign flips:

\[
x > \frac{-4}{-2}
\]

This simplifies to:

\[
x > 2
\]

### Step 3: Graph the solution on the number line
- Draw a number line.
- Place an open circle at \(x = 2\) to indicate that \(2\) is not included in the solution.
- Shade the number line to the right of \(x = 2\) to show that \(x > 2\).

### Step 4: Write the solution in interval notation
The solution in interval notation is:

\[
(2, \infty)
\]

This indicates that \(x\) can be any number greater than 2.

Would you like to see the graph or need any more details?

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Here are five related questions you might be interested in:
1. How do you solve a compound inequality?
2. What happens if the inequality is \(-2x + 9 \leq 5\)?
3. How do you solve absolute value inequalities?
4. What is the difference between a strict inequality and a non-strict inequality?
5. How do you solve a quadratic inequality?

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

Learn how to solve the inequality -2x + 9 < 5 with a detailed step-by-step solution. This problem covers key algebraic concepts such as inequalities and linear equations, along with representation on the number line. Suitable for students in Grades 7-9.

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