how do you solve this problem?

Question

11b -16 _< 12b +20

Answer 1

Move the variable terms to one side of the inequality and the constants to the other side, and then solve for the variable value:

11b -16 ≤ 12b + 20
-16 - 20 ≤ 12b - 11b
-36 ≤ b which is equivalent to b ≥ -36

So b is any number greater than or equal to -36. Plug -36 and any number greater than that into the inequality. If a true statement results, we have the right answer.

11(-36) -16 ≤ 12 (-36) + 20
-396 - 16 ≤ -432 + 20
-412 ≤ -412
Which is true.

Let b = -30, which is greater than -36. Then:

11b -16 ≤ 12b + 20 ----> 11 (-30) - 16 ≤ 12 (-30) + 20
11(-30) - 16 ≤ 12(-30) + 20
-330 -16 ≤ -360 + 20
-346 ≤ -340
Which is also true.

Now, plug a number less than -36 into the inequality and see what happens. Let b = -40.

11b -16 ≤ 12b + 20 ----> 11 (-40) - 16 ≤ 12 (-40) + 20
11(-40) - 16 ≤ 12(-40) + 20 ?
-440 -16 ≤ -480 + 20 ?
-456 ≤ -460 ?
No! -456 ≥ -460 !

So, our solution was correct, and b ≥ -36.

Answer 2

inequality