Solve the equation: $\frac{1}{3}x$ + $\frac{2}{5}$ = $\frac{3}{4}x$ - $\frac{1}{6}$

Step 1: Collect the x-terms on one side and the numbers on the other

(1/3)x + 2/5 = (3/4)x − 1/6

2/5 + 1/6 = (3/4)x − (1/3)x

Step 2: Simplify each side

Left side: 2/5 + 1/6 = 12/30 + 5/30 = 17/30

Right side: 3/4 − 1/3 = 9/12 − 4/12 = 5/12, so the right side is (5/12)x

Step 3: Solve for x

(5/12)x = 17/30

x = (17/30) × (12/5) = 204/150 = 34/25

Check:

• Left: (1/3)(34/25) + 2/5 = 34/75 + 30/75 = 64/75
• Right: (3/4)(34/25) − 1/6 = 102/100 − 1/6 = 51/50 − 1/6 = 153/150 − 25/150 = 128/150 = 64/75 ✓

So x = 34/25, which is option E.

Tip: In equations with fractions, you can multiply every term by the LCM of the denominators (here 60) to clear them all at once: 20x + 24 = 45x − 10, so 34 = 25x, so x = 34/25. Also, watch for options like A (17/30), which is only a partial step and not the final answer.