Select the values that make the inequality start fraction, z, divided by, minus, 8, end fraction, ≥, 9

−8
z

≥9 true. Then write an equivalent inequality, in terms of zz.
(Numbers written in order from least to greatest going across.)
Answer
Attempt 1 out of 2

-88 -80 -75
-73 -72 -71
-69 -64 -56

1 answer

To solve the inequality \(\frac{z}{-8} \geq 9\), we start by multiplying both sides by \(-8\). When we multiply or divide by a negative number, we must reverse the inequality sign:

\[ z \leq 9 \times (-8) \]

Calculating the right side:

\[ z \leq -72 \]

Now we have the equivalent inequality \(z \leq -72\).

Next, we need to select the values from the provided list that satisfy the inequality \(z \leq -72\):

  • \(-88\) (satisfies)
  • \(-80\) (satisfies)
  • \(-75\) (satisfies)
  • \(-73\) (satisfies)
  • \(-72\) (satisfies)
  • \(-71\) (does not satisfy)
  • \(-69\) (does not satisfy)
  • \(-64\) (does not satisfy)
  • \(-56\) (does not satisfy)

The values that satisfy the inequality are:

\[ -88, -80, -75, -73, -72 \]

Therefore, the answer is:

Answer: \(-88, -80, -75, -73, -72\)
Equivalent inequality: \(z \leq -72\)