Question

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 me how to make this one step by step?

Answer 1

`3(x+2) > 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`