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How to Remember the Inverse Property

For every property, or operation, there is an opposite or inverse property. The opposite of addition is subtraction and the opposite of multiplication is division. In math, the inverse properties serve many purposes; checking math solutions and finding the value of variables are just some of the applications. The rule for the additive inverse is that for any real number, a, there is an opposite number, -a, so that when combined the two equal zero and the rule for multiplicative inverse is that for any number, a, there is also an opposite, 1/a, so that when combined the two equal one.

Instructions

  1. The Basic Rule

    • 1

      Examine the real number 5. According to the first part of the rule for the additive inverse property, you need to find its opposite number, which is -5.

    • 2

      Add -5 to the real number: 5 + (-5). The two signs in the expression, positive and negative, will cancel out to a subtraction sign: 5 - 5.

    • 3

      Solve the expression: 5 - 5 = 0. The second part of the rule for the additive inverse property states that the two real numbers will equal zero, so this math is correct.

    • 4

      Examine the real number 9. According to the first part of the rule of the multiplicative inverse property, there must be an opposite number. In fraction form, 9 is actually 9/1. So the inverse is 1/9.

    • 5

      Multiply the real number by its inverse: 9/1 x 1/9 = 9/9, which simplifies to 1. (When any number is divided by itself the solution is one.) The second part of the rule states the solution is one, so this math is correct as well.

    Putting the Rules to Use

    • 6

      Examine the equation 6 + 2x = 26. Your goal is to find the value of x. For example, get x on one side of the equation by itself and the value on the other side.

    • 7

      Notice the 6 one the left side of the equation. In this problem, 6 is positive, so use the inverse property subtraction to move it. Because x is already on that side, you want to move the 6 to the other side of the equation, using the inverse property.

    • 8

      Subtract 6 from the left side of the equation. Since it is an equation and, therefore, must remain equal throughout the entire process, you have to perform the operation to both sides of the equation. 6 - 6 + 2x = 26 - 6. Because of the additive inverse property 6 - 6 equals 0 for the expression 0 + 2x = 26 - 6.

    • 9

      Simplify the expression: 2x = 20.

    • 10

      Notice the coefficient 2 attached to the variable x. These two factors are multiplied together, so the inverse property is division.

    • 11

      Divide 2 from both sides of the equation: 2x ÷ 2 = 20 ÷ 2. Again, because of the multiplicative inverse property, 2 ÷ 2 = 1 for the expression 1x = 20 ÷ 2 and in math, the one is understood and is usually omitted from the problem for a simplified version x = 10.

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