Find the solution set for the following problem. 5 diminished by 3 times a number is at most 11.
a) {x | x ≤ -2}
b) {x | x ≥ -2}
c) {x | x ≤ 2}
d) {x | x ≥ 2}

B) {x | x ≥ -2}

Step-by-step explanation:

We have to find a number that when subtracted 3 times from number 5 will get a result that is ≤ 11.  We can make the following inequality out of what we know:

5 - 3x ≤ 11

We just have to isolate x:

5 - 3x ≤ 11

5 - 11 ≤ 3x

-6 ≤ 3x

-2  ≤ x

x ≥ -2

And you can verify it... by testing with

-1 ⇒ 5 - (-3) ≤ 11, 8 ≤ 11 YES

and -3 ⇒ 5 - (-9) ≤ 11, 14 ≤ 11 NO