Simplifying Expressions
What is the first step to simplify the following expression:
2/5 (15x - 30y) + 10x
What is 6x- 12y + 10x?
Solution: Use the distributive property.
Jessica rented 1 video game and 3 movies for a total of $11.50.
What equation represents what Jessica spent in d dollars to rent each movie?
What is 3d + 4.75=11.50 ?
Solve for x: 5x + 11 = -24
What is -7?
Solution
5x + 11 = -24
-11 -11
5x= -35
x = -7
Ben earns $9.00 per hour and $6.00 for each delivery he makes. He wants to earn more than $155.00 in an 8-hour workday. What is the least number of deliveries he must make to reach his goal?
What is 14?
Solve: 6d +72 > 155
The length of a shape is 4 times the width. What expression shows the length of the shape?
What is 4w?
What expression is equivalent to 7/2h - 3(5h-1/2)?
* Keep answers as improper fractions. *
What is -23/2h + 3/2 ?
Step 1: 7/2h - 15h+ 11/2
Step 2: -23/2h + 3/2
T-shirts for the Big Apple Fundraiser will cost $4.00 to make and there is a $25.00 delivery fee to have them delivered. There are also offering two different sized wristbands: a large one that will cost $5.00, and a small one that will cost $3.00 to make. Write an expression to represent the total cost of ordering t, T-shirts.
What is 4t + 25 ?
Solution: The cost of the wristbands is extraneous information (not needed to solve).
Solve: k/8 = 10.2
What is 81.6?
Solution: Using inverse operations, multiply both sides by 8.
Solve the following inequality: 2x – 2 > –8
What is x > -3?
Solution: Add 2 to both sides then divide both sides by 2.
The perimeter of a certain pentagon is 10.5 centimeters. Four sides of this pentagon have the same length in centimeters, h, and the other side has a length of 1.7 centimeters. What is the value of h?
What is 2.2?
Solution:
4h + 1.7 = 10.5
What expression is equivalent to: 3n-12?
What is 3(n-4) ?
Solution: The GCF of 3 and 12 is 3. Factor out the 3.
Collin had 82 DVDs. His mother bought him d more DVDs. Create the expression that shows how many DVDs Collin has now.
What is 82 + d?
Solve the following equation: 1/2(10x + 8) = –21
What is x = -5 ?
Solution:
Distributive property
5x + 4 = -21
James needs at least 80 signatures from students in his school before he can run for class president. He has 23 signatures already. He and two of his friends plan to get the remaining signature during lunch. If each person gets the same number of signatures, which inequality can James use to determine the minimum number of signatures each person should get so he can run for class president?
What is 3x + 23 ≥ 80 ?
A triangle has side lengths of (5.5x + 6.2y) centimeters, (4.3x + 8.3z) centimeters, and (1.6z – 5.1y) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
What is 9.9x + 1.1y + 9.9z ?
Solution: Add all the sides and then combine like terms.
What expression represents a factorization of 32m + 56mp?
What is 8m (4 + 7p) ?
Solution: GCF of 32 and 56 is 8. Also they have a common variable of m so that must be factored out as well.
The cost of oranges in a grocery store is directly proportional to the number of oranges purchased. Jerri paid $2.52 for 6 oranges. If p represent the cost, in dollars, and n represents the number of oranges purchased, what equation best represents this relationship?
What is p=0.42n ?
Solution: $2.52 divided by 6 is 0.42.
Solve: 8x + 10 – 6x + 4 = 24
What is x = 5?
Chris is trying to save more than $44.00 for a new shirt that he wants. He found $8.00 in his pocket so he put it in an envelope. He will put $2.00 into the envelope every week until he has more than $44.00 in the envelope. He wants to calculate how many weeks, w, he must save in order to have more than $44.00 What inequality represents this situation?
What is 2w + 8 > 44?
The width of a rectangle is 6 inches. The length of the rectangle is twice its width. What is the perimeter of the rectangle?
What is 40 inches?
Solution: Length is 6 2/3 x 2= 13 1/3
P= 2L + 2W
What is an equivalent expression to: 6(4x +3y)?
Solve for x: 0.5x + 78.2 = 287
What is 417.6?
Solution: Subtract 78.2 from both sides, then divide by 0.5.
Solve the following inequality:
-4x + 8 < 48
What is x < -10 ?
A trailer will be used to transport several 40-kilogram crates to a store. The greatest amount of weight that can be loaded onto the trailer is 1,050 kilograms. An 82-kilogram crate has already been loaded onto the trailer. What is the greatest number of 40-kilogram crates that can also be loaded onto the trailer?
What is 24?
Solution:
40x + 82 ≤ 1050
The circumference of a circle is 11. What is the area of the circle, in terms of pi?
What is 30.25pi ?
Solution:
C=pi x diameter
so the diameter is 11. Radius is 1/2 the diameter so it is 5.5
A= pi x r2