• 7.EE.A.1 — Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
  

  Expressions and Equations

  7.EE.A.1 — Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

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• 6.EE.A.3
  

  Expressions and Equations

  6.EE.A.3 — Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

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• 6.EE.A.4
  

  Expressions and Equations

  6.EE.A.4 — Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.

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• 7.NS.A.1
  

  The Number System

  7.NS.A.1 — Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

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Use the expression below to answer the questions that follow.

$${\frac{1}{3}x-2y-5x+8}$$

1. How many terms are there in the expression?
2. Which terms are “like terms”?
3. Are there any constants? If so, what are they?
4. What are the variables in the expression?
5. What are the coefficients in the expression?

Rewrite $${5x+3x}$$ and $${5x-3x}$$ by combining like terms.

1. Do this by expanding each term using addition.
2. Do this by factoring out a common factor and using the distributive property. 
3. Can you rewrite $${5x+3y}$$ and $${5x-3y}$$ by combining terms? Why or why not? Use reasoning from parts a and b to support you answer. 

Find the sum of $${\left ( 0.75x-12y \right )}$$ and $$(-5+6y-0.5x)$$. Show each step in your work and explain why each step is equivalent to the expression in the step before.