Select the values that make the inequality 7, z, ≥, minus, 7z≥−42 true. Then write an equivalent inequality, in terms of zz. -16 -11 -9
-7 -6 -5
-3 -1 4
To determine the values that make the inequality true, we need to substitute each value into the inequality and see if it holds.
For -16:
7(-16) ≥ -42
-112 ≥ -42 (True)
For -11:
7(-11) ≥ -42
-77 ≥ -42 (True)
For -9:
7(-9) ≥ -42
-63 ≥ -42 (True)
For -7:
7(-7) ≥ -42
-49 ≥ -42 (True)
For -6:
7(-6) ≥ -42
-42 ≥ -42 (True)
For -5:
7(-5) ≥ -42
-35 ≥ -42 (False)
For -3:
7(-3) ≥ -42
-21 ≥ -42 (False)
For -1:
7(-1) ≥ -42
-7 ≥ -42 (False)
For 4:
7(4) ≥ -42
28 ≥ -42 (True)
The values that make the inequality true are -16, -11, -9, -7, -6, and 4.
We can write an equivalent inequality in terms of z as -7z ≥ -42.
Note: Inequalities are often written with the variable on the left side, so it would be more common to write this as -7z ≤ 42.