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])

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asked Aug 11, 2024 139k views

1 Answer

Micro · Answer 1 · 2024-08-16T16:37:00+0000

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

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).