Answer:
b ≤ -6 ✅
Explanation:
To solve an inequality, we will solve just like a normal equation. The goal is to isolate b, so we can determine the set of values it can take on.
Step 1: Add 5.3
We need to reverse the operation - 5.3, so we add 5.3.
-1.2b - 5.3 + 5.3 ≥ 1.9 + 5.3
-1.2b ≥ 7.2
Step 2: Divide by -1.2
We need to reverse the multiplication that is multiplying b by -1.2, so we will divide. However, we must remember an important rule first.
Important: When we divide by a negative number in an inequality, we must reverse the inequality sign, so ≥ becomes ≤.
-1.2b / -1.2 ≥ 7.2 / -1.2
b ≤ -6 (remember to reverse the sign!)
Step 3: Check
We now substitute our answer in and see if it is correct. We will use a number that is smaller than -6, for example, -8.
-1.2(-8) - 5.3 ≥ 1.9
9.6 - 5.3 ≥ 1.9
4.3 ≥ 1.9 ✅
We can check again with -6, since this and all numbers smaller than it should be a solution set.
-1.2(-6) - 5.3 ≥ 1.9
7.2 - 5.3 ≥ 1.9
1.9 ≥ 1.9 ✅
b ≤ -6 ✅