Question

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

Answer 1

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

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

Calculating \( (5.83)^2 \):

\[
(5.83)^2 = 33.9889
\]

Now, we can rewrite the inequality:

\[
4x + 1 \leq 33.9889
\]

Next, we subtract 1 from both sides:

\[
4x \leq 33.9889 - 1
\]

\[
4x \leq 32.9889
\]

Now, we divide both sides by 4:

\[
x \leq \frac{32.9889}{4}
\]

Calculating \( \frac{32.9889}{4} \):

\[
x \leq 8.247225
\]

Therefore, \( x \) can be any value less than or equal to approximately 8.25. Among the provided options, the only values that satisfy this inequality are:

- 8
- 9 (not valid since 9 > 8.25)
- 9.5 (not valid since 9.5 > 8.25)
- 10 (not valid since 10 > 8.25)

The only value for \( x \) that makes the inequality true is:

**8**