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

Question

Responses

9.5
9.5

10
10

9
9

8
8

Answer 1

To solve the inequality \( \sqrt{4x + 1} \leq 5.83 \), we will first square both sides to eliminate the square root.

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

2. Calculate \( (5.83)^2 \): \[ (5.83)^2 = 33.9889 \]

3. Now, substitute this value back into the inequality: \[ 4x + 1 \leq 33.9889 \]

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

5. Divide both sides by 4: \[ x \leq \frac{32.9889}{4} \approx 8.247225 \]

Now that we have determined \( x \) must be less than or equal to approximately \( 8.25 \).

Among the options provided:

• 9.5 (too high)
• 10 (too high)
• 9 (too high)
• 8 (valid, since \( 8 \leq 8.25 \))

The only value for \( x \) that satisfies the inequality \( \sqrt{4x + 1} \leq 5.83 \) is:

8