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9.6 Chapter summary

  • To solve a linear equation, we do the same thing to both sides of the equation to get the variable on its own.
  • An additive inverse is a number that results in the answer \(0\) when added to the original number.
  • A multiplicative inverse is a number that results in the answer \(1\) when multiplied by the original number.
  • The multiplicative property of \(1\) states that the product of any number and \(1\) is that number. For example, \(25 \times 1 = 25\).
  • The additive property of \(0\) states that the sum of any number and \(0\) is that number. For example, \(100 + 0 = 100\).
  • A reciprocal is the inverse (or opposite) of a value. The product of the number and its reciprocal is equal to \(1\).
  • There are many different ways that you can solve linear equations. These three steps will always get you to the right answer:
    • Simplify each side of the equation (remember order of operations).
    • Get the variables on the left hand side.
    • Use inverse operations to isolate the variable.