Lesson 6: Identify Equivalent Algebraic Expressions6.AT.7

I can…

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

Key words

• Equivalent Expressions — Expressions that look different but have the same value for every allowed variable value.
• Equivalent — Expressions that always have the same value.
• Simplify — To rewrite an expression in a shorter form that is still equal to the original.
• 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.
• Commutative Property — The order of the numbers can change in addition or multiplication without changing the result.
• Associative Property — The grouping of the numbers can change in addition or multiplication without changing the result.
• Counterexample — One test value that shows two expressions are not equivalent.

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

Mom writes 5k + 7 + 2k − 3 for the cost of k bags of fruit. Which expression is equivalent?

Check your answer

7k + 4

5k + 2k = 7k and 7 − 3 = 4, so the simplified expression is 7k + 4.

Sentence starter

I know ___ because ___.

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