Expressions
4(x - 5) =
4x - 20
3(x - 2) = 9
x = 5
Solve using elimination:
-7x - y = 13
8x + y = -14
x = -1
y = -6
What is a variable?
An unknown quantity represented by a letter
Find the value of two numbers if their sum is 12 and their difference is 4.
x = 8
y = 4
a(b + c) =
ab + bc
2(x – 3) + 5 = 3(x – 1)
x = 2
Solve for x and y by elimination:
-5x + 9y = -12
3x + 2y = 22
x = 6
y = 2
What does GCF stand for?
Greatest Common Factor
Find two numbers if their sum is 19 and their difference is 5.
x = 12
y = 7
-(x + 5 - 3x) + 7 =
2x + 2
(1/2)x + (3/4)x = 50
x = 40
Solve for x and y by substitution:
2x - y = 17
x - y = 10
x = 7
y = -3
What is a coefficient?
A number in front of (being multiplied by) a variable
There are 13 animals in the barn. Some are chickens and some are pigs. There are 40 legs in all. How many of each animal are there?
Chickens: 6
Pigs: 7
Find the GCF of the following terms:
4x2
24x
36x3
4x
-1 = (5 + x)/6
x = -11
Solve for x and y by substitution:
-2x + y = 10
4x - y = -14
x = -2
y = 6
What is a constant?
A number that is not being multiplied a variable
All 231 students in the Math Club went on a field trip. Some students rode in vans which hold 7 students each and some students rode in buses which hold 25 students each. How many of each type of vehicle did they use if there were 15 vehicles total?
Vans: 8
Buses: 7
Factor: 2x3 + 4x2 + 6x
2x(x2 + 2x + 3)
8 + (1/4)x = 3
x = -20
Solve for x and y:
−3x − 3y = 3
5x = -y − 17
x = -4
y = 3
What is a polynomial?
a collection of terms
Your school sold 100 tickets for a school play. An adult ticket costs $4, and a student ticket costs $1. The total amount of money earned from ticket sales was $196. How many adult and student tickets did your school sell?
Adult: 32 tickets
Student: 68 tickets