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Substitution Lessons

In algebra, letters such as x or y are used to represent values which are usually unknown. They can be used in equations or expressions to help solve a wide variety of problems. In many cases you may know the value of a variable. This is the case with the problem below:

b = 3, c = 18
5b - 2c + c / b

Since the values of both b and c are known, a numeric value for the expression can be found through the process of substitution.

When a school teacher becomes ill, a substitute teacher usually fills in for a few days. The substitute teacher temporarily takes the place of the usual teacher so that classroom activities may continue. Similarly, when using the method of substitution in algebra, a variable such as x or y is replaced with its value. The expression can then be simplified even further.

In this problem we replace the variables b and c since their values are given. Everywhere in the problem where the variable b is present, it is substituted with 3 in parentheses. Everywhere c appears, it is substituted with 18 in parentheses. It is important that the substituted number is placed in parentheses so that negative values are handled properly.

5(3) - 2(18) + (18) / (3)

Now, this expression can be simplified like any other.

The insides of all of the parentheses are simplified, and there are no exponents in the expression, so you can skip to simplifying multiplication and division in the order they appear.

15 - 36 + 6

Now simplify addition and subtraction in the order they appear (combine like terms):


Proceed to the next page to begin simplifying a more complex expression.

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