Solving Equations
3x+3=9
x=2
reflexive property
x=x
x+y-x+1
y+1
John has 3 times as many apples as Sarah. If Sarah has 4 apples, how many does John have?
12
|-7|
7
3(x-2)=12
x=6
Associative property of addition
-2x+y+3-4y+5
-2x-3y+8
The sum of two numbers is 12, and one number is 4 more than the other. What are the numbers?
4 and 8
∣x−5∣=3
x=8
x=2
2x-3=4x+5
x=-4
Distributive property
x(y+z)= xy+xz
-a-3(2x-3)-2a+9
-6x-3a+18
A taxi company charges a flat rate of $5 plus $2 per mile. Write and solve an equation to find the total cost for a 10-mile ride.
C(x)=5+2x
Total cost = 25
∣2x+4∣=6
x=1
x=-5
4x-x+3=3x+2x-2
x=5/2
Transitive property
if a=b, and b=c, then a=c
-(x+3)-2+5x(4-2)+1
9x-4
The product of two consecutive integers is 56. Find the integers.
x(x+1)=56
answer: 7 and 8
∣4x+1∣=9
x = 2
x= -5/2
4x(3-5)+2= -3(x-5)
Substitution property
3x = 3(4)
-4y(4-9)-4y+9(y+5)-3
25y+42
The sum of three consecutive integers is 102. Find the integers.
x+(x+1)+(x+2)=102
answers: 33, 34, 35
∣4x+1∣-3=9(2)
x=-11/2
x=5