Solving Linear Equations Math Example 5

Follow the full solution, then compare it with the other examples linked below.

Example 5

hard
Solve 2x+13=x−22\frac{2x + 1}{3} = \frac{x - 2}{2}.

Solution

  1. 1
    Cross-multiply or multiply both sides by 6 (LCD): 2(2x+1)=3(x−2)2(2x + 1) = 3(x - 2).
  2. 2
    Expand: 4x+2=3x−64x + 2 = 3x - 6.
  3. 3
    Subtract 3x3x: x+2=−6x + 2 = -6.
  4. 4
    Subtract 2: x=−8x = -8.
  5. 5
    Check: 2(−8)+13=−153=−5\frac{2(-8)+1}{3} = \frac{-15}{3} = -5 and −8−22=−102=−5\frac{-8-2}{2} = \frac{-10}{2} = -5 ✓

Answer

x=−8x = -8
When an equation has fractions, multiply every term by the least common denominator to clear denominators before solving.

About Solving Linear Equations

The process of finding the value of the variable that makes a linear equation true, using inverse operations to isolate the variable on one side of the equals sign. A linear equation has the variable raised only to the first power, producing exactly one solution.

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