Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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### Solving Inequalities for Squares

**Instructions:**

Input your inequality answers in the following format. Do not use spaces and do not input units.

- If your solution is \( x > 4 \), input the solution as \( x>4 \)
- If your solution is \( x \leq 3 \), input the solution as \( x<=3 \)

**Problem:**

If \( x \) is the length of one side of a square, then find values of \( x \) in meters for which the area of the square is less than 64 square meters.

**Solution:** 

1. **Determine the area of the square:** The area \( A \) of a square with side length \( x \) is given by the formula \( A = x^2 \).
2. **Set up the inequality:** Since the area must be less than 64 square meters, we set up the inequality:
   \[
   x^2 < 64
   \]
3. **Solve the inequality:** 
   \[
   x < 8 \quad \text{(taking the positive square root)}
   \]
   
Therefore, the length \( x \) of one side of the square must satisfy \( x < 8 \).

**Answer in required format:**

\[ x<8 \]

Please enter your answer in the provided input field and then proceed to the next page.
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Transcribed Image Text:### Solving Inequalities for Squares **Instructions:** Input your inequality answers in the following format. Do not use spaces and do not input units. - If your solution is \( x > 4 \), input the solution as \( x>4 \) - If your solution is \( x \leq 3 \), input the solution as \( x<=3 \) **Problem:** If \( x \) is the length of one side of a square, then find values of \( x \) in meters for which the area of the square is less than 64 square meters. **Solution:** 1. **Determine the area of the square:** The area \( A \) of a square with side length \( x \) is given by the formula \( A = x^2 \). 2. **Set up the inequality:** Since the area must be less than 64 square meters, we set up the inequality: \[ x^2 < 64 \] 3. **Solve the inequality:** \[ x < 8 \quad \text{(taking the positive square root)} \] Therefore, the length \( x \) of one side of the square must satisfy \( x < 8 \). **Answer in required format:** \[ x<8 \] Please enter your answer in the provided input field and then proceed to the next page.
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