Which of the following values for x makes the inequality 4x+1−−−−−√ ≤5.83 true?(1 point)%0D%0AResponses%0D%0A%0D%0A8%0D%0A8%0D%0A%0D%0A9.5%0D%0A9.5%0D%0A%0D%0A10%0D%0A10%0D%0A%0D%0A9

Answer 1

To solve the inequality \( \sqrt{4x + 1} \leq 5.83 \), we can start by squaring both sides to eliminate the square root. Remember to consider that squaring both sides of the inequality is valid here since both sides are non-negative when dealing with square roots.

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

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

3. Set up the inequality: \[ 4x + 1 \leq 33.9889 \]

4. Subtract 1 from both sides: \[ 4x \leq 33.9889 - 1 \] \[ 4x \leq 32.9889 \]

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

Now we need to determine which of the given options satisfies this condition:

• 8: This is less than 8.247225, so it satisfies the inequality.
• 9.5: This is greater than 8.247225, so it does not satisfy the inequality.
• 10: This is also greater than 8.247225, so it does not satisfy the inequality.
• 9: This is greater than 8.247225, so it does not satisfy the inequality.

The only value that satisfies the inequality \( \sqrt{4x + 1} \leq 5.83 \) is \( \boxed{8} \).