Question

1 here is an inequality: -3x > 18.
a. list some values for x that would make this inequality true
b. how are the values that make the inequality -3x ≥ 18 true different from the values that make -3x > 18 true?

Explanation:

Step1: Solve the inequality for x

Divide both sides by -3, reverse inequality sign:
$\frac{-3x}{-3} < \frac{18}{-3}$
$x < -6$

Step2: Identify valid values for part a

Pick numbers less than -6.

Step3: Compare inequalities for part b

Solve $\-3x \geq 18$: $\frac{-3x}{-3} \leq \frac{18}{-3}$ → $x \leq -6$
Compare to $x < -6$.

Answer:

a. Some valid values for $x$: $-7$, $-8$, $-10$, $-6.5$
b. The values that make $\-3x \geq 18$ true include $x = -6$, while the values that make $\-3x > 18$ true do not include $x = -6$ (they only include values strictly less than -6).