# Evaluating

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

40

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.

32x

32(8)

256

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.

78

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|

|-76|

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

144

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