Substitution

Evaluating Expressions with Substitution

Sports

• We substitute player for player in sports to give breaks. In order to substitute with the best outcome, you want to make sure they play the same position.

• It is the same thing with expressions. When we substitute, we will put in a number for the letter that it is equal to. The number and the letter are playing the same position.

• Example: If x=4, we can plug 4 in anywhere we see an x.

Multiple Choice

In sports, you substitute players into different positions then they usually play.

• True

• False

Multiple Select

Select all of the options that are examples of substitution.

• 3x, x=4, so 3(4)

• 3y, x=2, so 3(2)

• 2+x, x=2, so 2+2

• 2+y, x=4, so 2+4

Substituting and Evaluating

When you are given a number to plug in a variable's place, you are able to evaluate an expression.

Example 1: 3x; x=4; would give you 3(4), which equals 12.

Example 2: 3x+2y; x=5, y=4; so 3(5)+2(4)= 15+8=23

Multiple Choice

x+2y; x=3, y=7

when you substitute and evaluate this problem, your answer is 17.

• True

• False

Order of Operations Review

You MUST use the order of operations to evaluate correctly.

Please Excuse My Dear Aunt Sally (PEMDAS)

Parenthesis, Exponents, Multiply/Divide, Add/Subtract

*Be sure to write this at the top of every problem and check off each step as you go.

*Remember Multiply/Divide are whichever you see first left to right. This is the same for add/subtract.

Order of Operations Example (PEMDAS)

•  $2x+3y^3$  , x=4, y=2

• First, substitute.  $2\left(4\right)+3\ \left(2\right)^3$  

• Any parenthesis? No, except where we substituted.

• Any Exponents? Yes. Complete first.  $2^3=2\times2\times2=8$  Now replace with your answer.

• 2(4)+3(8)

• Any Multiplication/Division? Yes. Complete left to right. 2(4)=8, 3(8)=24

• 8+24; Final step add/subtract. 8+24= 32, so 32 is your answer.

Multiple Choice

Review Check:
Evaluate the following when x=2 and y=3
$$x^3+2y-3$$  

• 11

• 9

• 28