AlgebraStructure & Method · Book 1All Chapters

Fractional Equations

7-3Equations with Fractional Coefficients

Overview

Multiply both sides by the LCD to clear fractions, then solve.

Key ideas

  • Identify the LCD of all denominators.
  • Multiply every term by the LCD.
  • Solve the resulting linear equation.

Worked examples

Example 1

Problem. Solve x/2 + x/3 = 5.

Solution. Multiply by 6: 3x + 2x = 30 → 5x = 30 → x = 6.

Practice

Try each one. Click Show answer when ready.

  1. 1.

    Solve x/3 − x/4 = 2.

  2. 2.

    Solve (x + 1)/2 = 4.

  3. 3.

    Solve x/5 + 1 = 4.

Challenge problems

A little tougher — great for test prep. Click Show answer when ready.

  1. 1.

    Solve: (2/3)x + (1/4) = (5/6).

  2. 2.

    Solve: (3x − 1)/2 = (x + 5)/4.