which of the following values for x makes the inequality sqrt 4x+1 ⪯ 5.83 true

Answer 1

To solve the inequality $\sqrt{4x+1}\le 5.83$, we first square both sides (since both sides are non-negative):

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

Calculating $(5.83{)}^2$:

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

Thus, the inequality becomes:

$$4x+1\le 33.9889$$

Next, we subtract 1 from both sides:

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

Now, we divide both sides by 4:

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

So, the solution to the inequality is:

$$x\le 8.247225$$

Any value for $x$ that is less than or equal to approximately 8.25 will make the inequality $\sqrt{4x+1}\le 5.83$ true.