Solve the inequality and describe the solution set.

Question

The problem is below

 

  y – 6 ≥ 12

Answer 1

Add 6 to both sides of the inequality. 

 

  y-6+6>=12+6

 y>=18

 

You are done. 

 

Treat the inequality like an equation. What ever you do to one side you must do to the other side. The important difference is if you multiply by a negative number the inequality flips. Less than becomes greater than. Less than or equal to becomes greater than or equal to. And a greater than sign flips to a less than sign. 

Answer 2

y - 6 ≥ 12

 

Add 6 to both sides:

 

y ≥ 18

 

<----|----|----|----|----|----|----|----|----|----|----[----|----|----|----|----|----|--->

      -2     0      2     4     6     8    10    12   14  16  18    20   22    24   26   28    30

 

[18,∞)

 

The solution set contains all values of y greater than or equal to 18.