Equivalent Expressions 4.4

Goal To simplify expressions and recognize when two expressions are equivalent.

Wait a minute? What does it mean when two things are equivalent?

How do we write “Not equivalent”? ≠

Steps Simplify both expressions Once they are in their most simple form, determine if they are the same.

Remember… How do we know if an expression is in its most simple form? Answer: There are no like-terms (because you have already combined them)

Example 1 Are −2(𝑥+4)+5 and −2𝑥−4 equivalent? Let’s find out! We need to simplify. −2𝑥−3≠−2𝑥−4 so not equivalent

Example 2: YOU TRY! 𝐴𝑟𝑒 3+7 𝑥−2 𝑎𝑛𝑑 7𝑥−11 𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡? Answer: Yes!

New type of problem. You are going to be asked to “rewrite in intercept form”. What is intercept form? All you have to do is simplify 

Example Rewrite 𝑦=5+3(𝑥−3) in intercept form. Answer: 𝑦=3𝑥−4

How does this relate to our goal? Why do we care? This shows us that we may have an equation that looks unfamiliar to us, but if we simplify it, it actually is something we are very comfortable with (y=mx+b)

You try! Rewrite 𝑦=11−2(𝑥+4) in intercept form. Answer: y= -2x+3

A little trickier… Rewrite 4𝑦−𝑥=4 in intercept form.

You try Rewrite 3𝑦−6𝑥=9 in intercept form.

Team Competition/Homework