Solve the inequality and graph the solution on the line provided.

4, x, plus, 9, is less than or equal to, minus, 11

4*x*+9≤

−11

To solve the inequality \(4x + 9 \leq -11\), follow these steps:

1. **Subtract 9 from both sides** of the inequality to isolate the term with \(x\):
   \[
   4x + 9 - 9 \leq -11 - 9
   \]
   Simplifies to:
   \[
   4x \leq -20
   \]

2. **Divide both sides by 4** to solve for \(x\):
   \[
   \frac{4x}{4} \leq \frac{-20}{4}
   \]
   Simplifies to:
   \[
   x \leq -5
   \]

### Solution:
The solution to the inequality is \(x \leq -5\).

### Graphing the Solution on the Number Line:

1. Draw a number line.
2. Mark the point \(-5\) on the number line.
3. Since \(x\) is less than or equal to \(-5\), draw a solid circle at \(-5\) to indicate that \(-5\) is included in the solution.
4. Shade the number line to the left of \(-5\) to represent all numbers less than or equal to \(-5\).

Would you like a detailed explanation of any part, or do you have any questions?

Here are 5 related questions to deepen your understanding:

1. How would the solution change if the inequality were \(4x + 9 < -11\)?
2. What is the solution to \(4x + 9 = -11\) (an equation rather than an inequality)?
3. How do you solve the inequality \(4x + 9 \geq -11\)?
4. What happens to the inequality when you divide both sides by a negative number?
5. How do you graph the inequality \(x \geq -5\) on a number line?

**Tip:** When graphing inequalities, a solid circle indicates the number is included in the solution (\(\leq\) or \(\geq\)), while an open circle indicates it is not included (\(<\) or \(>\)).

Learn how to solve the inequality 4x + 9 ≤ -11 with a detailed step-by-step guide. This problem covers key algebraic concepts, including solving linear inequalities and graphing on a number line. Suitable for students in Grades 7-9.

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