Simplifying Expressions
9 + 5r - 9r - 12
-4r - 3
Solve. Show your steps algebraically.
40 - 5n = -5
n = 9
Show an algebraic equation that models the word problem and solve. Final answer should be in a complete sentence.
Liam's phone company charges a monthly charge of $12.95 and $0.25 per minute during calls. Liam's monthly phone bill comes out to $21.20. How many minutes were charged on this bill?
Equation: 0.25m + 12.95 = 21.20
Liam was charged for 33 minutes in this bill.
Simplify the expression:
-10v + 6r2 -2v - + 3r
6r2 - 12v + 3r
Solve for e. Show your steps algebraically.
-26e + 891 = -71
e = -37
Joaquin is a hotel manager. His responsibilities include renting rooms for conferences. The hotel charges $250 per day plus $15 per person for the grand ballroom. How many people could attend a wedding reception in the grand ballroom if the wedding planners have a budget of $4,000?
Equation: 250 + 15x = 4,000
Answer: 250 people can attend the wedding reception in the grand ballroom.
Simplify the Expression:
-8 (-5b + 7) + 5b - 8
45b - 64
Solve for x. Show your steps algebraically.
6 - 15 + -1 = -5x - 1 + 6x + 9 - 9x
x = 2.25
The perimeter of a rectangle is 108 in. The length is 4 more than 4 times the width. Find the length and the width the rectangle.
Simplify the expression:
-4p - (1 - 6p) + 11 - 2p
10
Solve for k. Show your steps algebraically.
3k - 3 (4 + 2k) = -25 - 5
k = -6
A car rented for $29 per day plus $0.08 per mile. Sam paid $46.12 for a one-day rental. How far did Sam drive?
Equation: 29 + 0.08x = 46.12
Answer: Sam drove 214 miles with his rental car.
Simplify the expression:
5(-10 + 9m) - 2(1 + 7m)
-52 + 31m
Solve for n. Show your steps algebraically.
0.7n - 1.5 + 7.3n = -14.5
n = -2
The width of a rectangle is 12 cm less than the length. If the perimeter is 156 cm, find the dimensions of the rectangle.
Equation: 156 = 2x + 2 (x - 12)
Answer: The length is 45cm. The width is 33cm.
Simplify the expression:
-1.2 (4.2x + 2.2) + 3.1
-5.04x + 0.46
Solve for p. Show your steps algebraically.
8 1/14 = -1 2/7p - 2 3/4 p
p = -2
Sophie bought three blouses at one price and 2 blouses priced $3 below the others. The total cost was $91.50. What is the price of the blouses?
Answer: The three blouses cost $19.50 and the other 2 blouses are $16.50
Simplify the expression:
4(-3/2n+1)-10/3
2/3 - 6n
Solve for p. Show your steps algebraically.
-3 1/4 (-9/2p + 2/3) = -60 2/3
p = -4
A triangle has a perimeter of 46 meters. The length of the second side is 5 meters more than the length of the first side. The third side is three meters less than twice the first side. How long is each side of the triangle?
Equation
x + (x + 5) + (2x - 3) = 46
x = 11 (First side)
The first side is 11m. The second side is 16m. The third side is 19 m