Vocabulary
Terms that have a common variable or exponent. (Same last name)
Like Terms
Simplify the expression.
32x + 8 – 34x
-2x + 8
Solve for x.
4x=16
x=4
Solve the inequality.
2.5g + 8 < 35
g < 10.8
The length of a rectangle is five less than three times the width. The perimeter is 102 feet. Find the dimensions of the rectangle.
Equation: 8w - 10 = 102
x= 14
Multiplying the number on the outside of the parentheses by everything on the inside. (Rainbow method)
The Distributive Property
Simplify the expression
-(4.5k - 2)
-4.5k + 2
Solve for x.
7x - 28 = 14
x = 6
Solve the inequality.
-25d + 360 > 1,400
d < -41.6
Stephanie is registering her son for swim lessons. This is a one-time $45 registration fee, plus a $20 fee per lesson. Stephanie paid a total of $225. For how many lessons did Stephanie register?
Equations: 45 + 25x = 225
x=9
An unknown number.
Variable
Simplify the expression
-7(3z + 5t – 3g)
-21z -35t + 21g
Pedro made lemonade for some friends. He served 34 ounces to his friends and then measured that there were 20 ounces leftover. How much lemonade did Pedro make?
Equation: x - 34 = 20
x=54 ounces
Solve the inequality.
190m + 175 > 5,340
m > 27.18
Mr. Martinez rented a car for one day. The price was $42, plus $0.15 per mile. If the total cost of the rental was $75, how many miles did he drive?
Equations: 42 + 0.15x = 75
x= 220 miles
The number in front of the variable.
Coefficient
Simplify the expression
28r – 9(2r + 6)
-26 - 18r
Solve for x.
-4k + 9 = 32
k = -5.75
Aliana has a leak in her shower. A plumber charges a $75 diognostic fee plus $50 per hour of labor. Aliana has no more than $375 set aside for home emergencies. How many hours (h) of plumbing work can Aliana afford with her emergency fund?
Inequalities: 50h + 75 </= 375
h </= 6
Three brothers each purchase two chili dogs and an order of tater tots. The tater tots cost $2.50. If their grand total was $34.50, then how much did each chili dog cost?
Equation: 3(2x + 2.50) = 34.50
x= $4.50
The name of a number without a variable.
Constant
Simplify the expression.
8 - 0.5(6t + 2)
-3t + 7
Solve for x.
-2(1.7x + 1.2) - 3.8 = 4
x= -3
Katie is raising money for her softball team by selling quarts of strawberries for $6 each. Her Nana has already donated $25 towards the fundraiser, and each team member is trying to raide at least $150. How many quarts of strawberries (s) will katie need to sell to reach this goal?
Inequality: 6s + 25 >/= 150
s >/= 20.83
21 quarts
Mrs. Perkins hosts a birthday party for her son and 7 guests. She orders 2 cookies and a cupcake for each child. The cost of the cupcake is $2.75, and the total bill is $46.00. What is the cost of a cookie?
Equation: 8(2x + 2.75) = 46
x= $1.50