Question

Select the values that make the inequality -z ≤ 8 true.

Then write an equivalent inequality, in terms of z.
(Numbers written in order from least to greatest going across.)

Answer 1

The values that satisfy the inequality -z ≤ 8 are those where z is greater than or equal to -8. The equivalent inequality in terms of z is z ≥ -8.

Step-by-step explanation:

To select the values that make the inequality -z ≤ 8 true, we look for the values of z that satisfy the condition when z is negated.

In other words, the inequality tells us that the value of z must be greater than or equal to -8 when the negative sign in front of z is considered.

To find an equivalent inequality in terms of z without the negative sign, we multiply both sides by -1, remembering that this reverses the inequality sign: z ≥ -8.

This means that any value of z greater than or equal to -8 satisfies the original inequality. The equivalent inequality is simply the original inequality with the sign reversed, indicating that z lies to the right of or exactly at -8 on the number line.