Evaluating Expressions by Substitution at a Glance

Remember that a variable is like an empty box that's waiting for a number. Have you ever seen a box wait? Those things have unbelievable staying power.

We call it substitution when we put a number into the box.

Sample Problem

What's the value of 4x + 5 when x = 3?

Let's break it down: 4x + 5 is the same as 4 · ☐ + 5, so write 3 in the box:

4(3) + 5

After substituting values for the variables in an expression, we can evaluate the expression by working out the arithmetic.

4(3) + 5 =
12 + 5 = 17

Long story short: to substitute a value for a variable, replace every copy of the variable with the value enclosed in parentheses.

Sample Problem

What's the value of 2y + y² when y = 4?

Here we go: replace every occurrence of y with 4:

2(4) + (4)²

4ou see? What did 4ou say? We can stop now? Oh. Thank 4ou.

2(4) + (4)² =
8 + 16 = 24

Be Careful: Make sure to put parentheses around values when substituting for variables. There can be some mix-ups with negative signs otherwise. We don't want no more mix-ups. Not after that failed bank heist. You hear that, Ira?