Question

Solve the inequality 6b-24+3(b-4)<0 and express the solution in interval notation.

a) (-[infinity], 4)
b) (-[infinity], 8)
c) (4, [infinity])
d) (8, [infinity])

Answer 1

The solution to the inequality 6b - 24 + 3(b - 4) < 0 is (4, [infinity]) (C).

Step-by-step explanation:

First, distribute the 3 inside the parentheses: 6b - 24 + 3b - 12 < 0.

Combine like terms: 9b - 36 < 0.

Add 36 to both sides to isolate the term with b: 9b < 36.

Divide both sides by 9: b < 4.

So, the solution is b < 4. In interval notation, this is (4, [infinity]), which corresponds to option (c).