Unit 3 Expressions Assignments

Which expressions are equivalent to 7x - 14? Check all that apply.

-(14 - 7x) 7(x - 2) 3x - 14 + 4x

In order to make the expression below equivalent to 1/2x + 6, which additional operation should be included in the expression? Use the drop-down menu to select the operation.

-3x/4

Which is equivalent to 1/4x?

1/8x+1/8x

Peter plans to build a tree house in his back yard. He needs to know how many square feet of lumber he should buy for the floor. He considers the greatest number of people who will be in the tree house at one time, and decides to allow 20 square feet of floor space per person. Which expression can Peter use to determine the size of the floor, in square feet, if n represents the number of people?

20n

Peter is going to put up 5 walls in the tree house. Each wall will be 7 feet high and 7 feet across. He wants to leave room for windows that measure 2 feet by 2 feet. Which algebraic expressions will give the total square feet of lumber he will need for the walls if n represents the number of windows he puts in? Choose all that apply.

245 - 4n 49(5) - 4n (7)(7)(5) - 4n (7)(7)(5) - (2)(2)n

Peter bought 90 boards for $270. Which algebraic expression represents the cost of n boards? How much would it cost to buy 20 boards?

3n $60

Which expression is not equivalent to the other three?

4 + 7x - 2

Each side of the tree house is the same length. Peter plans on putting a pentagonal roof on the tree house. The sides of the roof will be 6 inches longer than the sides of the tree house. Which expression represents the perimeter of the roof, in inches?

5n + 30

Peter decides to put carpet on the floor of his tree house. The area of the floor can be found by the expression , where s equals the side length and h equals the distance from the center to the side. Peter approximates these measures, as shown on the diagram. If the tree growing through the center of the house takes up 25 ft2 of floor area, how many square feet of carpeting will Peter need?

80ft

Peter wants to use 75-watt lightbulbs and other electronics in his tree house. He has one outlet with a maximum of 900 watts. Which expression represents how much wattage remains if n is the number of lightbulbs turned on?

900 - 75n

Peter wants to put 2 coats of paint on both the inside and outside of the walls. There are 5 walls, each side having 45 ft2 of paintable surface. A gallon of paint covers x ft2. Explain how to write an expression to represent the number of gallons of paint Peter needs.

Both sides of one wall would be 90 square feet. Two coats of paint for both sides would be 180 square feet. There are 5 walls, so the total square feet to be painted is 5(180) = 900. So, Peter needs 900/x gallons of paint.

Peter figures he can build the entire tree house by himself in 20 hours. He figures that each additional friend who helps him would improve the time by 10%. He created a table using the algebraic expression n - n(0.10), where n is the previous number of hours. To the nearest tenth of an hour, how long will it take to build the tree house if 4 friends are helping?

It will take 13.1 hours.

Peter is at a lumber yard. He gets 2 free boxes of nails for every 10 boards he buys. Write an expression for the number of boxes of nails Peter will get if he buys n boards. If each box has 100 nails, explain how to write an expression to find how many nails Peter will have if he purchases 90 boards.

The algebraic expression n/10, where n is the number of boards, represents the number of times he gets 2 free boxes of nails. So 2(n/10), or n/5, is the number of boxes, and 100(n/5), or 20n, is the number of nails. Substituting 90 in for n, Peter will get 1,800 nails.

Ryan is trying to determine whether 2.7x - 5.9 is equivalent to 2.8x - 5.9. To test this, he substitutes 0 for x into both expressions. Explain why this will not give him the correct answer.

The coefficients of x are different in the expressions, but the constant values are the same. Zero times any value is zero, so both expressions will be equal to -5.9. If Ryan tried any other number, he would see that the expressions are not equivalent.

Write an expression having only two terms that is equivalent to 2x - 3. Explain how you wrote the expression and how you can check that it is equivalent.

The expression -3 + 2x is equivalent to 2x - 3. I know it is equivalent because for every value of x that is substituted in, the two expressions simplify to the same value. I took the expression and used the commutative property to not change the value.

The tree house will be 8 feet off the ground. Peter will hang a rope, with knots tied for foot holds. Each knot uses an additional 2 inches of rope. Write an expression for the length of the rope needed if Peter ties n knots and wants the rope to touch the ground. How many inches of rope are needed if there are 8 knots? Explain.

The tree house is 8 feet off the ground, or 96 inches up because (8)(12) = 96. Each knot needs 2 extra inches, so the expression for the length of rope needed is 96 + 2n. If n = 8, then Peter will need 96 + 2(8) = 112 inches of rope.

Use the model to create zero pairs. What is an equivalent expression that has two terms?

x+1,x + 1,1+x,1 + x