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Algebra 1 · Unit 1 · Micro-Lesson 7

Use Patterns to Rewrite Expressions

I canuse patterns I recognize to rewrite an expression in an equivalent form.
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Why should I care?

Connect the Math to Real Life

Equivalent expressions let us choose the form that makes a calculation, comparison, or real-world situation easier to understand.

A phone plan written as 25 + 10d + 5d is easier to understand after combining the matching data charges: 25 + 15d.

Important words

Build the Vocabulary

Read the meaning, then connect it to the example.

Equivalent expressions

Different-looking expressions that have the same value for every allowed variable value.

Structure

How the numbers, variables, operations, and groups in an expression are organized.

Rewrite

Show the same mathematical value in a different form.

See the pattern

Worked Examples

Combine a pattern
8x + 3 + 2x = 10x + 3

The x-terms match, so their coefficients combine. The constant stays separate.

Show a repeated group
(t + 4) + (t + 4) = 2(t + 4)

Both forms represent two identical ticket-and-snack bundles.

Try it yourself

8-Question Practice

Choose an answer, check your thinking, and use the hint if you need another try.

0 correct
1

Rewrite 6x + 4x + 9.

2

A plan costs $20 plus 7d for data and 3d for extra data. Which simpler expression is equivalent?

3

Which rewrites three copies of (m + 5)?

4

Which expression is equivalent to 9a − 2a + 6?

5

Which pattern should you notice first in 4y² + 3y + 5y²?

6

Rewrite 2(p + 6) as repeated groups.

7

Why are 5x + 8 and 13x not equivalent?

8

Which rewrite makes the total easiest to see: 4 tickets at t dollars plus 4 fees of $2?

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