Definition: Equivalent expressions are expressions that have the same value for every value of their variables, even if they look different.
What are equivalent expressions?
Two expressions are equivalent when they give identical results for any number substituted in. They can be different in form.
How do you create them?
Use properties: distribute, combine like terms, or factor. The expression 3(2x + 5) – 4x becomes 6x + 15 – 4x, which simplifies to 2x + 15.
How do you test them?
Substitute a value. For x = 4, the original is 3(13) – 16 = 23, and 2x + 15 = 23. They match. One match does not prove equivalence, but a mismatch proves they differ.
Why use different forms?
Some forms reveal more. The form 5(x + 3) shows a factor, while 5x + 15 shows separate terms. If Mathbot is charged for 5 tickets that each cost x plus a 3 dollar fee, both forms give the same total.
What are factoring examples?
12a + 18 = 6(2a + 3), where 6 is the greatest common factor.
What is a common mistake?
Thinking x + x equals x2. Adding gives 2x, while multiplying x by x gives x2.