To solve the inequality \( \sqrt{4x + 1} \leq 5.83 \), we first square both sides to eliminate the square root (keeping in mind that squaring is valid because both sides are non-negative):
\[ 4x + 1 \leq (5.83)^2 \]
Now we calculate \( (5.83)^2 \):
\[ (5.83)^2 = 33.9889 \]
So now our inequality becomes:
\[ 4x + 1 \leq 33.9889 \]
Next, we subtract 1 from both sides:
\[ 4x \leq 33.9889 - 1 \] \[ 4x \leq 32.9889 \]
We then divide both sides by 4 to isolate \( x \):
\[ x \leq \frac{32.9889}{4} \] \[ x \leq 8.247225 \]
Now we will determine which of the given options is less than or equal to approximately 8.25:
- 9.5 (not valid)
- 8 (valid)
- 9 (not valid)
- 10 (not valid)
The only value from the options that makes the inequality \( \sqrt{4x + 1} \leq 5.83 \) true is:
\[ \boxed{8} \]
1 answer