Simplifying Algebraic Expressions
Simplify the expression:
5x -2(x + 1/2)
What is 3x - 1?
An item is on sale for 30% off of it's original price. What is the new price of the item if it's original price was $56? Write an expression and solve.
What is 56 - 0.3(56) = 39.20 or 0.7(56) = 39.20?
Shelby is creating a budget for the week. She earns $15.50 per hour. Her rent costs $300, she wants to have more than $280 in her banking account. How many hours should Shelby work? Write an ineqality and solve.
What is $15.50h - $300 > $280?
Shelby should work more than 37.4 hours
Solve for n:
5(n - 4) = -60
What is n= -8?
Mrs. Jensen wrote this expression on the board and asked her class to simplify it. What is the simplified expression?
4.75x + (-0.2y) + 1/4x + 1/2y
What is 5x + 0.3y?
Simplify: -5x -5(-3x - 1)
What is 10x + 5?
Jenny says that -2(x + 3y+ 0.5) is equivalent to -2x -6y - 1. What are two things that she can do to determine if these expressions are equivalent?
What is, Jenny can use the distributive property to expand the first expression and she could substitute the same values for x and y in each expression to determine if they are equivalent.
Kendra has a bead collection, she currently has 2300 beads and would like to have at least 3500 beads. Her favorite beads come in packages of 200. Write and solve an inequality that would show the number of packages of beads (b) Kendra wishes to buy.
What is 2300 + 200b ≥ 3500. The number of packages of beads b≥6?
Solve for t:
-3t + -8 = 25
What is t = -11?
Kristen found a jacket that had a 30% markdown on it. If the price of the jacket is represented by j, how much does the jacket cost? (excluding sales tax)
What is j - 0.3j or 0.7j?
A picture frames width is 2 cm less than its length. Write a simplified expression that represents its perimeter in terms of its lenght (L). (Hint: Draw a picture)
What is 4L - 4? or 4(L-1)
A trapezoid has two equal side lengths, each represented by x, the top of the trapezoid is x + 6 and the bottom is 3x - 4, what is the perimeter of the trapezoid? (Hint: draw a picture)
What is x + x + x + 6 + 3x - 4, or 6x + 2?
In the cafeteria, there is one large 12-seat table and many smaller 4-seat tables. There are enough tables to fit no more than 200 students. Write an inequality whose solution is the possible number of 4-seat tables in the cafeteria.
What is 12 + 4n ≤200?
What is n ≤ 47
Solve for p:
7p - 8 = -22
What is p = -2?
Kenny makes $7.50 an hour at his job. Last week, he worked 20 2/3 hours. He deposits $120 dollars in the bank, and wants to use the rest of the money to buy lottery tickets. If the lottery tickets are $3 a piece, how many lottery tickets can he buy?
What is Kenny can buy 11 tickets?
Simplify this expression:
-5(x + 1/5y)
What is -5x-y?
A rectangle has a length of 3x + 2 and a width of 2x. Write an expression that shows the perimeter of the rectangle in simplest form.
What is 10x + 4 or 2(5x + 2)?
Sandra is 10 years old. When 6 is subtracted from Kelly's age and 1/3 of the difference is taken, the result is equal to Sandra's age. Write an equation to determine how old Kelly is, use k as the variable.
What is 1/3(k - 6) = 10? Kelly is 36 years old.
Solve for j:
2/5( j + 40) = -4
What is j = -50?
Sally designs web pages for customers. She charges $135.50 per web page; however, she must pay a monthly rental fee of $650 for her office. Write an expression to determine her take-home pay after expenses. If Sally designed 5 web pages last month, what was her take-home pay after expenses?
What is $135.50x - 650?
$135.50(5) - 650 = 25
Sally's take-home pay after expenses is $27.50
Simplify this expression:
6(-3x -12 + y)
What is -18x + y -72?
Write this expression in factored form: -4x + 28
What is -4(x - 7) or 4(-x + 7) or 4(7 -x)?
A mover is loading an elevator with many identical 48-pound boxes (b). The mover weighs 185 pounds. The elevator can carry at most 2000 pounds. Write an inequality to go with this problem and solve for b the number of boxes that can be in the elevator.
What is 185 + 48b less than or equal to 2000?
b less than or equal to 37.8125
Solve for w:
4(w + 1) = -6
What is w = -10/4 or -5/2?
Sampson is attending Karate classes. Each class costs $7 plus a one-time registration fee of $20. Let the variable n represent the number of classes Sampson can take if he budgeted $150 for Karate. Write an expression and solve for the number of classes Sampson can take.
What is 20 + 7n = 150, Sampson can take 18 classes?