Final answer:
The equivalent inequality to 3 4/x > x 2/x is x < 6.
Step-by-step explanation:
To solve the inequality 3 * 4/x > x * 2/x, we first simplify the expressions on both sides.
On the left side, we multiply 3 by 4/x, and on the right side, we simply have x multiplied by 2/x.
Since we have a common factor of x in the denominators on both sides, we can multiply through by x (assuming x is not equal to 0) to clear the fractions.
The inequality then becomes:
12 > 2x
Next, we can solve for x. Dividing both sides by 2 yields:
6 > x
S,o the equivalent inequality is x < 6.