Question

3 the opposite of z is greater than 5.
a. what are two possible values of z? what are two values that z cannot be?
what must be true about all possible values of z? show your work.

Explanation:

Step1: Translate to inequality

The opposite of $z$ is $-z$, so:
$-z > 5$

Step2: Solve for $z$

Multiply both sides by $-1$ (reverse inequality):
$z < -5$

Step3: Identify possible values

Choose numbers less than $-5$:
$z = -6$, $z = -7$

Step4: Identify impossible values

Choose numbers $\geq -5$:
$z = 0$, $z = -3$

Answer:

• Two possible values of $z$: $-6$ and $-7$
• Two values $z$ cannot be: $0$ and $-3$
• All possible values of $z$ must be less than $-5$ ($z < -5$)