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Unit 3 Test Review Chapter 5 Lessons 1-8

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**5-1 To evaluate an algebraic expression:**

1.) Plug in the value for each variable and rewrite the expression 2.) Follow order of operations to solve (show work step by step)

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**Evaluate each expression**

3m² ̶ 4 if m = -3 6s ̶ 3t if s = 4 and t = -2

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**Write expressions from word problems**

Key words like each and per tell you where variable should go and to multiply Look for other key words to tell you what operation to use

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**Nicole has d dollars in her bank account**

Nicole has d dollars in her bank account. On her birthday, she received $150 from family and friends to put into her account. Write an expression to represent the total amount of money now in her account.

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**Andy is buying some T-shirts and shorts for his wardrobe**

Andy is buying some T-shirts and shorts for his wardrobe. Each T-shirt costs $14 and each pair of shorts costs $18. Write an algebraic expression to represent the total cost of buying x T-shirts and y pairs of shorts. Find the total cost of buying 4 T-shirts and 3 pairs of shorts.

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**Mitchel bought c cups for $6 each. Jennifer bought d cups for $6 each**

Mitchel bought c cups for $6 each. Jennifer bought d cups for $6 each. Write an expression that can be used to find the total amount Mitchel and Jennifer spent for the cups.

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5-2 Need to know what an arithmetic sequence is and be comfortable describing the pattern and continuing the pattern

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**5-3 NEED TO KNOW THE 5 PROPERTIES IN LESSON 3!**

Commutative Property (+ or x) Associative Property (+ or x) Additive Identity Multiplicative Identity Multiplicative Property of Zero

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**Name the property shown by each statement.**

1.) 6 + (b + 2) = (6 + b) + 2 2.) 1 x 4 = 4 3.) 7 + t = t + 7

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5-4 Need to know how to rewrite expressions using the Distributive Property If you have a negative number on outside of parentheses and subtraction sign on inside of parentheses, ___________________ Don’t forget to distribute to the second term inside the parentheses!

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**Use the Distributive Property to rewrite each expression**

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**5-5 Simplifying Algebraic Expressions STEPS:**

1.) Get rid of all subtraction signs (keep, change, opposite) 2.) Distribute to get rid of parenthesis (if needed) 3.) Show the like terms (circle, underline, box) 4.) Simplify *List variable terms first and alphabetically

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**Write each expression in simplest form**

1.) -4x x – 6 2.) x – 4 – 12x – 9

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**Write each expression in simplest form**

3.) -3x – 4(5x + 7) 4.) 6(4a + 3b) – 8a

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**Identify the terms, like terms, coefficients, and constants in each expression.**

1.) 9 – 5x – 2 + x 2.) -y + 4 – 7y

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**5-6 Add linear expressions STEPS:**

1.) Get rid of subtraction signs (keep, change, opposite) 2.) Distribute if needed 3.) Rewrite without parentheses and show like terms 4.) Simplify

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Add 1.) (10x – 5) + (-6x + 4) 2.) (-8y – 2) + 3(-4y – 7)

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Write a linear expression in simplest form to represent the perimeter of the triangle. Find the perimeter if the value of x is 4 inches.

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**The table gives the number of laps Pragitha swam each week**

The table gives the number of laps Pragitha swam each week. Write an expression in simplest form for the total number of laps she swam all four weeks. Week 1 2 3 4 Laps x + 2 3x 2x + 1 4x – 6

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**5-7 Subtract Linear Expressions STEPS:**

1.) Put a 1 after the subtraction sign in the middle of the two expressions 2.) Get rid of subtraction signs 3.) Distribute -1 to the second expression 4.) Add like terms and simplify

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Subtract. 1.) (12x + 8) ̶ (x – 2) 2.) (3x – 2) ̶ (5x – 4)

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**Jacob has (4n + 7) crayons. Maria has (3n + 2) crayons**

Jacob has (4n + 7) crayons. Maria has (3n + 2) crayons. Write an expression to show how many more crayons Jacob has than Maria. Then evaluate the expression if n = 6.

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**The table gives the cost of a gallon of gasoline at two stations**

The table gives the cost of a gallon of gasoline at two stations. How much more does gasoline cost at Gas For Less than at Cut-Rate? Cut-Rate –2x + 3.5 Gas for Less x – 1.2

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**5-8 Factor Linear Expressions STEPS: 1.) Find GCF of both terms**

2.) Divide both terms by GCF and put in parentheses 3.) Put GCF outside of parentheses *Use Distributive Property to check (Don’t forget about bday cake shortcut)

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**Factor each expression**

1.) 12x ) 90x – 15

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A sidewalk has an area that can be represented by the expression (8x + 24) feet. Factor the expression 8x + 24.

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