How to Solve Two-Step Equations With Fractions (Step-by-Step)

To solve a two-step equation with fractions, multiply every term by the least common denominator (LCD) to clear the fractions, then undo addition/subtraction and multiplication/division to isolate the variable. This turns a messy fraction equation into a clean two-step problem you already know how to solve.

Below we walk through two fully solved examples, the exact method in five steps, and the mistakes students most often make.

Worked Example 1: Solve (x/3) + 2 = 7

1. Identify the LCD. The only denominator is 3, so the LCD is 3.
2. Multiply every term by 3: 3·(x/3) + 3·2 = 3·7, which gives x + 6 = 21.
3. Undo the addition. Subtract 6 from both sides: x = 15.
4. Check. (15/3) + 2 = 5 + 2 = 7. ✓

Answer: x = 15.

The Method in 5 Steps

1. Find the LCD of all denominators. Example: for (x/4) − 1/2 = 3, the LCD is 4.
2. Multiply every term on both sides by the LCD. This clears the fractions completely.
3. Simplify. You should now have a two-step equation with integer coefficients, like 2x + 5 = 11.
4. Isolate the variable. First undo addition/subtraction, then undo multiplication/division.
5. Check your answer by substituting it back into the original equation.

Worked Example 2: Solve (2x/5) − 1/2 = 3/2

1. Find the LCD. The denominators are 5, 2, and 2. The LCD is 10.
2. Multiply every term by 10:
   • 10 · (2x/5) = 4x
   • 10 · (1/2) = 5
   • 10 · (3/2) = 15
   The equation becomes 4x − 5 = 15.
3. Add 5 to both sides: 4x = 20.
4. Divide both sides by 4: x = 5.
5. Check. (2·5/5) − 1/2 = 2 − 1/2 = 3/2. ✓

Answer: x = 5.

Common Mistakes

• Multiplying only some terms by the LCD. Every term on both sides must be multiplied — including whole numbers and terms without fractions.
• Adding fractions with unlike denominators without finding a common denominator. Clearing fractions with the LCD avoids this entirely.
• Reversing the order of operations. Undo addition/subtraction before multiplication/division when isolating the variable.
• Forgetting to distribute the sign when the fraction is being subtracted. For example, in x/2 − (x−1)/3, the numerator (x−1) must stay grouped.
• Skipping the check. A quick substitution catches sign errors and arithmetic slips.

Once the pattern clicks, two-step fraction equations become as fast as regular two-step equations — the LCD does almost all the heavy lifting. If you want a tutor that catches your sign errors mid-problem and asks you the next question instead of just handing you the answer, sign up and try LernOS.