Question

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

9.5
9.5

8
8

10
10

9

Answer 1

To solve the inequality \( \sqrt{4x + 1} \leq 5.83 \), we can start by squaring both sides to eliminate the square root (keeping in mind that squaring both sides is valid as long as both sides are non-negative):

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

Calculating \( (5.83)^2 \):

\[
(5.83)^2 = 33.9889
\]

Now the inequality becomes:

\[
4x + 1 \leq 33.9889
\]

Next, subtract 1 from both sides:

\[
4x \leq 32.9889
\]

Now, divide both sides by 4:

\[
x \leq 8.247225
\]

Now we can evaluate the given options to see which one satisfies the inequality:

1. \( x = 9.5 \) : not valid (since \( 9.5 > 8.247225 \))
2. \( x = 8 \) : valid (since \( 8 \leq 8.247225 \))
3. \( x = 10 \) : not valid (since \( 10 > 8.247225 \))
4. \( x = 9 \) : not valid (since \( 9 > 8.247225 \))

From this analysis, the only value that satisfies the inequality \( \sqrt{4x + 1} \leq 5.83 \) is:

**8**