Sometimes variables are used in place of numbers. It is possible that the variable could be replaced with different values in some expressions.

When we replace the variable with a value, we call this evaluating. Check out a couple of examples:

Example 1: 32 + x, where x = 8

Here we will rewrite the expression, but we will replace the x with an 8 and carry out the operation.

32 + x

32 + 8


Example 2: 32x, where x = 8

When faced with an example that has numbers next to letters, don't fall into the trap of just replacing the x with the 8 and calling the answer 328!

This is a common mistake. Instead, when we see numbers next to variables, we need to multiply.




Example 3: 5x + 7y, where x = 3 and y = 9

In this problem, we have two different variables to replace. Be sure to carefully replace the x value with the 3 and the y value with the 9. In addition, you need to use the correct order of operations when simplifying.

5x + 7y  Replace the variables with the given values.

5(3) + 7(9)   Next, we will multiply.

15 + 63  The last steps is to add.


Evaluating can become more difficult when exponents, integers, and other additional symbols are added in. Let's take a look at just a few more examples of the different types you might come across.

Example 3: |5m - 11|, where m = -13

Notice that in this example, we have absolute value bars around the expression.

To start, we will first evaluate the expression inside the absolute value bars.

|5(-13) - 11|

|-65 - 11|


Next, we will take the absolute value of the expression. Remember that the absolute value is the distance from zero and distances are positive.

|-76| = 76

Example 4: 3g2 + 8h, where g = -4 and h = 12

Remember that after you replace the variables with the values given, you need to use the order of operations in order to complete the process.

3g2 + 8h

3(-4)2 + 8(12)

3(16) + 8(12)

48 + 96


Example 5: 11 + k(3j - 7), where k = -2 and j = 5

Again, we will start by replacing the variables with the values.

11 + k(3j - 7) Start by replacing the variables with the values given.

11 + -2(3(5) - 7) Next, we will multiply inside the parentheses.

11 + -2(15 - 7) Complete the parentheses by subtracting next.

11 + -2(8) Here is the tricky step. Be sure to multiply -2 by 8.

11 - 16 Now we will subtract.

-5 Notice that the answer is a negative because we were taking
 away more than we had.

You might have noticed that as soon as you have replaced the variable with the value, you can solve the rest of the problem like a typical order of operations question.

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