Lesson 6: Equivalent Expressions6.AT.7

I can…

I can show that two expressions are equivalent by simplifying and combining like terms.

Key words

• Equivalent — Expressions that always have the same value.
• Simplify — To write an expression in a shorter, simpler way.
• Like Terms — Terms with the same letter raised to the same power, like 2x and 5x.
• Combine — To add or subtract terms with the same letter into one.
• Coefficient — The number in front of a letter, like the 3 in 3x.

Steps

1. Producer A wrote 3x + 2x + 10 and Producer B wrote 5x + 10. Are they equivalent?
2. I test x = 4. For A: 3(4) + 2(4) + 10 = 12 + 8 + 10 = 30.
3. For B: 5(4) + 10 = 20 + 10 = 30.
4. Both give 30, and 3x + 2x is just 5x, so they are equivalent.

Try it

Which expression is equivalent to 6n + 4 + 3n − 1?

Check your answer

9n + 3

6n + 3n = 9n and 4 − 1 = 3, so the simplified expression is 9n + 3.

Sentence starter

I know ___ because ___.

Goal: I can explain my work using the words equivalent, simplify, like terms, and combine.