At a Glance - Evaluating Expressions by Substitution
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.
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.
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?
What's the value of the expression 5x + 11 when x = 3?
What's the value of 3y2 + 3y if y = 2?
If y = -4, what's the value of the expression 2y + y2?
Evaluate -3x + 4 for x = -2.
Evaluate for x = 10.
Evaluate 4x2 for x = -1.
Evaluate 5y – 3y2 for y = -2.
Evaluate z3 – 18 + z for z = -2.
Evaluate 4xyz + x + y – z for x = 2, y = 3, and z = 5.
Evaluate b2 – 4ac for a = 1, b = 3 and c = -2.