Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26 what is the solution set of this problem?

a. (- infinity, - 21)
b. (- infinity, - 21]
c. [- 21, + infinity)
d. (21, + infinity)

b. (- infinity, - 21]

Step-by-step explanation:

Let x be the unknown number. Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26.

5 × (x + 27) ≥ 6 × (x + 26)

We apply the distributive property.

5x + 135 ≥ 6x + 156

135 - 156 ≥ 6x - 5x

-21 ≥ x

x is less than or equal to -21. The solution set of this problem is

(- infinity, - 21].

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