Grade 9 · Math · Algebra 1

9th grade Name the property, and give the reason for each step in solving an equation worksheet

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Name the property, and give the reason for each step in solving an equation

Grade 9 Math Worksheet

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Circle the best answer, or write your answer on the line.

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Line 1
3x − 4 = 5 − (x − 7). Line 2: 3x − 4 = 12 − x. Line 3: 4x − 4 = 12. Line 4: x − 1 = 3. Line 5: x = 4.
1.
Milo solves 3x − 4 = 5 − (x − 7) in five lines. What is the reason for going from line 2 to line 3?
- Subtraction property of equality
- Distributive property
- Addition property of equality
- Division property of equality
2.
x/2 + x/3 = 10. Line 2: (5/6)x = 10. Line 3: x = 12. Noah solves x/2 + x/3 = 10 in three lines. What is the reason for going from line 1 to line 2?
- Distributive property, which combines like terms
- Addition property of equality
- Multiplication property of equality
- Commutative property of addition
Line 1
2x − 3 = 5x + 9. Line 2: −3 = 3x + 9. Line 3: −12 = 3x. Line 4: −4 = x.
3.
Pia solves 2x − 3 = 5x + 9 in four lines. What is the reason for going from line 1 to line 2?
- Distributive property
- Division property of equality
- Subtraction property of equality
- Addition property of equality
4.
Ren rewrites (3x)(4) as 12x. Which properties of numbers allow this?
- Distributive property
- Just the associative property of multiplication
- Commutative and associative properties of multiplication
- Just the commutative property of multiplication
5.
Tala rewrites 3x + 12 as 3(x + 4). Which property of numbers allows this?
- Commutative property of multiplication
- Distributive property
- Identity property of multiplication
- Associative property of multiplication
6.
Zee solves (x − 3)(x + 4) = 0 and writes x − 3 = 0 or x + 4 = 0. Which property allows this?
- Distributive property
- Multiplication property of equality
- Zero-product property
- Identity property of multiplication
7.
Ari rewrites 12 = 3x as 3x = 12. Which property of equality allows this?
- Transitive property of equality
- Commutative property of multiplication
- Symmetric property of equality
- Reflexive property of equality
Esme has 3(x + 4) = 27 and divides both sides by 3. The left side becomes x + 4. What does the right side become?
Luz has x/5 − 3 = 4 and adds 3 to both sides. The left side becomes x/5. What does the right side become?
Noah has −2x + 7 = 15 and subtracts 7 from both sides. The left side becomes −2x. What does the right side become?

9th grade Name the property, and give the reason for each step in solving an equation worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Name the property, and give the reason for each step in solving an equation. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can name the property that makes a rewrite true (for example, commutative or distributive).
I can give the reason for a step in solving an equation: do the same thing to both sides.
I can find the first line with a mistake in a worked solution.

Standard: A-REI.A.1 (A-SSE.A.2 supports)

Words to know

property: A rule that is always true for numbers, such as swapping the order of an addition.

commutative: Two pieces trade places and the total stays the same.

associative: The pieces keep their order and only the brackets move.

identity: Adding 0 or multiplying by 1 leaves the number the same.

inverse: A number and its opposite make 0 (or a number and its flip make 1).

property of equality: Do the same thing to both sides and the equation stays true.

Common mistakes

Your child mixed up swapping the order with regrouping.

Your child mixed up the property that keeps a number the same with the one that makes 0 or 1.

Your child named the operation that is in the equation, but the step undoes it.

What to say

Ask: in this step, did the numbers trade places or did the brackets move?

Ask: does the number stay the same, or does it become 0 or 1?

Ask: what was done to both sides to get the letter alone?

Questions parents ask

What is the most common mistake with name the property, and give the reason for each step in solving an equation?

Your child mixed up swapping the order with regrouping.

How can I help my child with name the property, and give the reason for each step in solving an equation?

Ask: in this step, did the numbers trade places or did the brackets move?

Are these 9th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More algebra 1

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