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

Question

Responses

9.5
9.5

8
8

9
9

10
10

Answer 1

To solve the inequality $\sqrt{4x+1}\le 5.83$, we first square both sides to eliminate the square root (keeping in mind that squaring is valid because both sides are non-negative):

$$4x+1\le (5.83{)}^2$$

Now we calculate $(5.83{)}^2$:

$$(5.83{)}^2=33.9889$$

So now our inequality becomes:

$$4x+1\le 33.9889$$

Next, we subtract 1 from both sides:

$$4x\le 33.9889-1$$ $$4x\le 32.9889$$

We then divide both sides by 4 to isolate $x$:

$$x\le \frac{32.9889}{4}$$ $$x\le 8.247225$$

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 $\sqrt{4x+1}\le 5.83$ true is:

$$\boxed{{\displaystyle 8}}$$