Simplifying Expressions 1
-5n + 3(6 + 7n)
16n + 18
-8(b + 3)
-8b - 24
Each of the two congruent sides of an isosceles triangle has length 2x - 1.5, and the third side has length x + 3. Write an expression that shows the sum of the side lengths.
2x - 1.5 + 2x - 1.5 + x + 3
The perimeter of a square is given as 8x + 20. Write an expression for the perimeter using factoring based on the number of sides of a square.
4(2x + 5)
The captains of the soccer team describe ordering identical T-shirts for the team. Kimberlin says that the cost is $192. Alli says that the cost is 8t, where t is the number of T-shirts. Which person’s description tells how much each T-shirt costs? Explain your reasoning.
Alli's expression; 8t gives the cost of each T-shirt. The coefficient gives the cost of each T-shirt.
-2n - (9 - 10n)
8n - 9
n + 4 - 9 - 5n
-4n - 5
Each of the two congruent sides of an isosceles triangle has length 2x - 1.5, and the third side has length x + 3. Write an expression that shows factoring.
2(2x - 1.5) + x + 3
The perimeter of a square is given as 8x + 20. Write an expression for the perimeter.
2x + 5 + 2x + 5 + 2x + 5 + 2x + 5 or another equivalent expression
Mr. Ramirez orders one pair of drumsticks and one copy of sheet music for each student in his music group. One pair of drumsticks costs $1.50, and each copy of sheet music costs $3.50. He has z students. What does the expression 1.5z + 3.5z represent?
A) The expression represents the cost of one pair of drumsticks and one item of sheet music.
B) The expression represents the number of students that need supplies.
C) The expression represents the total cost as the sum of the costs of two different supplies for z students.
D) The expression represents the total cost per student as $5.
C
9a + 10(6a - 1)
69a - 10
5(-3p + 7) + 5(p - 1)
-10p + 30
Which of the following expressions are equivalent to 4x - 8? Select all that apply.
A) 2(2x - 8)
B) (2x - 4) + (2x - 4)
C) x + x + x + x + 2 + 2 + 2 + 2
D) 4(x - 2)
B, D
The perimeter of a square is represented by the expression 32x - 12.8. Draw a square and label its side lengths.
Each side should be labeled 8x - 3.2
An artist frames his rectangular painting. The length of his painting is 3 times the width, w. What expression shows that the length of the painting is 3 times the width.
2(3w + w)
10 - 5(9n - 9)
-45n + 55
-3 - 7(-3 - 6v)
18 + 42v
Which of the following expressions are equivalent to 4x - 8? Select all that apply.
A) 2(2x - 8)
B) (2x - 4) + (2x - 4)
C) x + x + x + x + 2 + 2 + 2 + 2
D) 4(x - 2)
Jesse chose A as his answer. How did he get that answer?
Jesse forgot to distribute 2 to both terms in the parentheses to get 4x - 16, which is not equivalent.
The perimeter of a square is represented by the expression 32x - 12.8. Write 3 equivalent expressions for the perimeter.
8x - 3.2 + 8x - 3.2 + 8x - 3.2 + 8x - 3.2
4(8x - 3.2)
2(16x - 6.4)
or equivalent expression
Write an expression for the following situation.
The total a cashier earns who works x hours each week for 2 weeks and earns $12.50 per hour
2x(12.50) or 25x
-7(n + 3) - 8(1 + 8n)
-71n - 29
-9(1 - 10n) - 2(3n + 9)
-27 + 84n
Six bakers use a total of 12x - 36 pounds of flour each hour. If each baker uses the same amount of flour, find an expression for the number of pounds each baker uses in an hour.
2x - 6
Six bakers use a total of 12x - 36 pounds of flour each hour. Write an expression equivalent to 12x - 36 to represent the total flour used in an hour.
2x - 6 + 2x - 6 + 2x - 6 + 2x - 6 + 2x - 6 + 2x - 6 or equivalent expression
Write an expression to represent the following situation.
The total cost for three people to go to a concert, when each person spends $25 for a ticket and $12.50 for a T-shirt.
3(25 + 12.50) or 3(37.50)