Which of the following values for x makes the inequality 4x+1−−−−−√ ≤5.83 true?(1 point)

Question

Responses

8
8

9.5
9.5

9
9

10

Answer 1

To solve the inequality \( \sqrt{4x + 1} \leq 5.83 \), we will first square both sides to eliminate the square root (keeping in mind this only works because both sides are non-negative):

1. Start with the original inequality: \[ \sqrt{4x + 1} \leq 5.83 \]

2. Square both sides: \[ 4x + 1 \leq (5.83)^2 \] \[ 4x + 1 \leq 33.9889 \]

3. Subtract 1 from both sides: \[ 4x \leq 32.9889 \]

4. Divide both sides by 4: \[ x \leq 8.247225 \]

Now, we need to find which of the given options for \( x \) satisfies this inequality:

• \( 8 \) is less than 8.247225 (valid)
• \( 9.5 \) is greater than 8.247225 (invalid)
• \( 9 \) is greater than 8.247225 (invalid)
• \( 10 \) is greater than 8.247225 (invalid)

The only value that makes the inequality true is: 8