Question

2 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 $-3x \geq 18$ 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

Any number less than -6 satisfies $x < -6$.

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. Example values: $x=-7$, $x=-8$, $x=-10$, $x=-6.5$ (any value less than -6 is valid)
b. The values for $-3x \geq 18$ include $x=-6$ (and all values less than -6), while the values for $-3x > 18$ only include values strictly less than -6 (excluding -6 itself).