Math 7 · Unit 4, Lesson 6: Equivalent Expressions · Tile 1 of 4
Same Value, Every Time
How to tell if two expressions are equivalent
How to tell if two expressions are equivalent
Equivalent expressions give the same answer for every number you put in. There are two ways to check. One: simplify both, and see if they match. Two: try a number in both. If even one number gives different answers, they are not equivalent.
Words we use
| Elle (math-speak) | Finn (plain English) |
|---|---|
| Equivalent | Equal in value. From Latin aequus, meaning equal, and valere, meaning to be worth. Equivalent expressions are worth the same. |
| Substitute | To put a number in place of the variable. A substitute teacher takes the place of your teacher. |
Elle and Finn
Two expressions are equivalent if they have the same value for every value of the variable.
Same answer, no matter what number you try. One mismatch, and they're not equivalent.
Careful: one matching number does not prove it. 2x + 2 and 4x both equal 4 when x = 1. But when x = 2, 2x + 2 = 6 and 4x = 8. Simplifying both is the proof. A test number can only catch a mismatch.
Elle and Finn talk it over
I tried x = 1, and they matched. Done!
Try x = 2.
Six and eight.
Lucky number one.
I'm never trusting number one again.
Trust it to catch mistakes, not to prove things.
Watch it work
Is 3(x + 4) − x equivalent to 2x + 12?
Is 5 − 2(x − 1) equivalent to 3 − 2x?
Catch it with x = 0: 7 and 3.
NC standards: NC.7.EE.2, NC.7.EE.1.