Solving Linear Equations Math Example 3

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Example 3

medium
Solve 2(3x−4)=5x+62(3x - 4) = 5x + 6.

Solution

  1. 1
    Step 1: Distribute on the left: 6x−8=5x+66x - 8 = 5x + 6.
  2. 2
    Step 2: Subtract 5x5x from both sides: x−8=6x - 8 = 6.
  3. 3
    Step 3: Add 8 to both sides: x=14x = 14.
  4. 4
    Check: 2(3(14)−4)=2(42−4)=2(38)=762(3(14) - 4) = 2(42 - 4) = 2(38) = 76 and 5(14)+6=70+6=765(14) + 6 = 70 + 6 = 76 ✓

Answer

x=14x = 14
First distribute to eliminate parentheses, then collect variable terms on one side and constants on the other. Always verify by substituting back into the original equation.

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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