The inequality \(3(x + 2) > 4(x - 3)\) is equivalent to which of the following inequalities?

F. \(x < -6\)
G. \(x < 5\)
H. \(x < 9\)
J. \(x < 14\)
K. \(x < 18\)

Can anyone explain how to solve this step by step?

4(x-3)\\\\3\cdot x+3\cdot2 > 4\cdot x+4\cdot(-3)\\\\3x+6 > 4x-12\ \ \ /-6\ \ \ /-4x\\\\3x-4x > -12-6\\\\-x > -18\ \ \ /:(-1) < 0\ then\ changing\ symbols\ >\ \to\ <\\\\x < 18\\\\Answer:K"> 3 ( x + 2 ) > 4 ( x − 3 ) 3 ⋅ x + 3 ⋅ 2 > 4 ⋅ x + 4 ⋅ ( − 3 ) 3 x + 6 > 4 x − 12 / − 6 / − 4 x 3 x − 4 x > − 12 − 6 − x > − 18 / : ( − 1 ) < 0 t h e n c han g in g sy mb o l s > → < x < 18 A n s w er : K

Answered by Anonymous | 2024-06-10

Option K. The correct equivalent inequality is option K: x < 18.
To solve the inequality 3(x + 2) > 4(x - 3),
Expand both sides of the inequality:
3(x + 2) = 3x + 6
4(x - 3) = 4x - 12
3x + 6 > 4x - 12
6 > x - 12
6 + 12 > x
18 > x
x < 18
Therefore, the inequality 3(x + 2) > 4(x - 3) is equivalent to x < 18. The correct answer is option K.

Answered by PhilDavis | 2024-06-25

The solution to the inequality 4(x - 3)"> 3 ( x + 2 ) > 4 ( x − 3 ) is x < 18 , which corresponds to option K.
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Answered by Anonymous | 2024-12-19