EXPLANATION
Given the system of inequalities:
-5(y-4) ≤ 30 or 18 + y < 20
Applying the distributive property:
-5y + 20 ≤ 30 or 18 + y < 20
Subtracting -2 to both sides of the first inequality and -18 to the second one:
-5y ≤ 30 - 20 or y < 20 - 18
Subtracting numbers:
-5y ≤ 10 or y < 2
Dividing both sides by 5 in the first inequality:
-y ≤ 10/5 or y < 2
Simplifying the first inequality:
-y ≤ 2 or y < 2
Dividing by -1 the first inequality and reversing:
y ≥ 2 or y < 2
In conclusion, the solution in interval notation is as follows:
(-∞,∞)
