Answer: x < -46/17
Explanation:
To solve the inequality:
1/3x - 1/4(x + 2) > 3x - 4/3
First, we simplify the left-hand side by finding a common denominator:
4(1/3x) - 3/4(x + 2) > 3x - 4/3
4/3x - 3/4x - 9/2 > 3x - 4/3
Next, we simplify the equation:
7/12x - 9/2 > 3x - 4/3
To isolate the variable x on one side of the inequality, we will move all the x terms to the left-hand side and all the constants to the right-hand side:
7/12x - 3x > 9/2 - 4/3
-17/12x > 23/6
Finally, we can solve for x by dividing both sides by -17/12, remembering to reverse the inequality because we are dividing by a negative number:
x < (23/6) ÷ (-17/12)
x < -46/17
Therefore, the solution to the inequality is:
x < -46/17