Question

first simplify both sides of each inequality. then determine whether the given statement is true or false.

\\\frac{15 + 6(4 - 1)}{3 \cdot 2 + 5} \ge 6\\

the inequality simplifies to \\(\square \\ \square \\ 6\\), so the given statement is \\(\square\\)

Explanation:

Simplify the numerator

$$ 15 + 6(4 - 1) = 15 + 6(3) = 15 + 18 = 33 $$

Simplify the denominator

$$ 3 \cdot 2 + 5 = 6 + 5 = 11 $$

Evaluate the fraction and the inequality

$$ \frac{33}{11} = 3 $$

$$ 3 \ge 6 \quad (\text{False}) $$

Answer:

First simplify both sides of each inequality. Then determine whether the given statement is true or false.

$$\frac{15 + 6(4 - 1)}{3 \cdot 2 + 5} \ge 6$$

The inequality simplifies to <blank>\(3\)</blank> <blank>\(\ge\)</blank> \(6\), so the given statement is <blank>false</blank>.