Question

Select the correct answer. Solve the following inequality. 21 ≤ -3(x − 4) < 30 A. -3 ≤ x < 6 B. -10 < x ≤ -3 C. 28 ≤ x < 37 D. -6 < x ≤ -3

Answer 1

D. -6 < x ≤ -3

Explanation:

21 ≤ -3(x − 4) < 30

21/3 ≤ -3(x − 4)/3 < 30/3

7 ≤ -(x − 4) < 10

7 ≤ -x - (-4) < 10

7 ≤ -x + 4 < 10

7 - 4 ≤ -x + 4 - 4 < 10 - 4

3 ≤ -x < 6

(3 ≤ -x < 6)/(-1)

-3 >= x > -6 ==> when dividing by a negative number, switch the inequality

sign

-6 < x ≤ -3 ==> D