Question

Which of the following values for x makes the inequality 4x+1−−−−−√ ≤5.83 true?(1 point) Responses 9 9 8 8 10 10 9.5

Answer 1

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

\[
4x + 1 \leq (5.83)^2
\]

Calculating \( (5.83)^2 \):

\[
5.83^2 = 33.9889
\]

Now, substituting this back into the inequality gives us:

\[
4x + 1 \leq 33.9889
\]

Next, we can subtract 1 from both sides:

\[
4x \leq 32.9889
\]

Now, divide both sides by 4:

\[
x \leq 8.247225
\]

So, the values for \( x \) that make the inequality true must be less than or equal to approximately 8.25. Looking at the provided options:

- 9
- 8
- 10
- 9.5

The only value that satisfies \( x \leq 8.25 \) is:

**8**