Hello from MrBillDoesMath!
Answer: x < 3
Discussion:
Let's solve (1/3)x + 2x > 3x - 2. Note that "x" occurs in three terms. Let's combine them by bringing all x's to one side of the equation. Subtract (1/3)x from the both sides:
(1/3)x - (1/3)x + 2x > 3x - 2 - (1/3)x or
2x > 3x - (1/3)x - 2.
Subtract 2x from both sides
2x - 2x > 3x - 2x - (1/3)x - 2 or
0 > x - (1/3)x - 2.
Add 2 to both sides:
0 + 2 > x - (1/3)x -2 + 2 or
2 > x - (1/3)x or
2 > x(2/3).
Multiply both sides by 3/2 to get:
2 * (3/2) > x (2/3) * (3/2) or
3 > x (1)
Thank you,
MrB
