Please show your work so I can understand The problem presented is as follows:**6. Solve the following inequality. Write the answer in interval notation.**\[\frac{9x - 4}{x + 2} \leq -5x\]To tackle the inequality, follow these steps:1. **Clear the Fraction**: Multiply both sides by \(x + 2\) (consider the sign changes due to \(x + 2\)).2. **Isolate Terms**: Bring all terms to one side to form a polynomial inequality.3. **Solve for Critical Points**: Set the numerator equal to zero and solve for \(x\), then consider points where the expression is undefined.4. **Test Intervals**: Use the critical points to establish intervals. Choose a test point from each interval and determine if it satisfies the inequality.5. **Consider Endpoint Behavior**: Include or exclude endpoints based on the inequality sign (≤ or <).6. **Write the Solution**: Express the solution in interval notation, combining intervals where the inequality holds true.Note that any graph or diagram related to this would involve plotting the intervals and points where the inequality holds true.

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Answered: Solve the following inequality. Write…

Math

Calculus

Solve the following inequality. Write the answer in interval notation. 9x - 4 x + 2 ≤-5x

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

Please show your work so I can understand

The problem presented is as follows:

**6. Solve the following inequality. Write the answer in interval notation.**

\[
\frac{9x - 4}{x + 2} \leq -5x
\]

To tackle the inequality, follow these steps:

1. **Clear the Fraction**: Multiply both sides by \(x + 2\) (consider the sign changes due to \(x + 2\)).

2. **Isolate Terms**: Bring all terms to one side to form a polynomial inequality.

3. **Solve for Critical Points**: Set the numerator equal to zero and solve for \(x\), then consider points where the expression is undefined.

4. **Test Intervals**: Use the critical points to establish intervals. Choose a test point from each interval and determine if it satisfies the inequality.

5. **Consider Endpoint Behavior**: Include or exclude endpoints based on the inequality sign (≤ or <).

6. **Write the Solution**: Express the solution in interval notation, combining intervals where the inequality holds true.

Note that any graph or diagram related to this would involve plotting the intervals and points where the inequality holds true.

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