• 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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• 7.NS.A.2
  

  The Number System

  7.NS.A.2 — Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

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In math class, students are attempting to simplify the expression written on the board:

$${7-2(3-8x)}$$

Three students make an attempt at a first step:

Len writes:  $${5(3-8x)}$$

Monty writes: $${7-2(-5x)}$$

Nailany writes:  $${7-6-16x}$$

1. Do you agree with any of the students? Explain your reasoning for each one.
2. Oscar is a little stuck, so he rewrites the problem in a different way to help him determine what to do. He writes $${ 7+(-2)(3-8x)}$$. How might this new expression help Oscar simplify the expression? 

Which expressions below are equivalent to $${4-3(6x-3)}$$? Select all that apply.

a.     $${(4-18)x+9}$$

b.     $${(4+9)-18x}$$

c.     $${4-(18x-9)}$$

d.     $${4-18x-3}$$

e.     $${4-18x+9}$$

f.     $${6x-3 }$$

Determine which expression is equivalent to $${\frac{3}{4}-x\left ( \frac{1}{2}-\frac{5}{8} \right )+\left ( -\frac{3}{8}x \right )}$$.

a.     $${-\frac{3}{4} x}$$

b.     $${\frac{1}{2} x}$$

c.     $${\frac{1}{8}-\frac{7}{8}x}$$

d.     $${\frac{3}{4}-\frac{1}{4}x}$$

Simplify the expressions.

a.     $${-2x+15-4(3x-1)}$$

b.     $${-(a+b)-\frac{3}{2}(a-b)}$$