Question

Which of the following inequalities have -8 in its solution set?

A. 0 < x+4 < 1


B. Three less than a number is at least -5 and at most 2.


C. The sum of 8 times a number and 7 is between -1 and 1.


D. 3x ≥ 24 or 3x ≤ -24

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Which of the following inequalities have -6 in its solution set?

A. 5x > 35 or 5x < −35


B. Two less than a number tripled is at least -5 and at most 1.


C. The sum of 3 times a number and 5 is between -16 and 11.


D. -8 < x−5 < 3

Answer 1

To determine when -8 is a solution, you will replace each variable with -8 and see which statements are true.

A. x + 4, -8 + 4 = -4, this is not in between 0 and 1
B. x - 3, -8 - 3 = -11, not between -5 and 2
C. 8x + 7, 8(-8) + 7 = -57 is not between -1 and 1
D. 3x, 3(-8) = -24 is equal to -24, so this one is true

A. 5x, 5(-6) = -30 is not less than -35 or greater than 35
B. 3x - 2, 3(-6) - 2 = -20 is not between -5 and 1
C. 3x + 5, 3(-6) + 5 = -13 is between -16 and 11
D. x - 5, -6 - 5 = -11 is not between -8 and 3