Integers
2x-1=13
x= 7
2.5x+31=66
x=14
14 = (3a + 6) + 2
a=2
x+5=16
x=11
What is the Inverse of Addition?
Subtraction
Anna started a dog walking business. So far she has $117. She spent $47 on supplies and charges $12 an hour. Write an equation to represent this situation.
12x-45=117
3 = 2 + 4x
x= 1/4
3.2x+2.6=-23
x=-8
-45 = x + 4
x = -7
2n+10 = 4
n = 2
What is the Inverse of Multiplication?
Division
The sum of 12 times a number and 180 is the opposite of 720.
12x+180=-720
4 = -28 + 8x
x= 4
(2x)/3 = -3
x= 9
4x + 3 = 7
x = 1
5(m-3) = 4
m = 19/5
What math operation does split mean?
Division
6 times a number and 12 is 36
6x+12=36
3x+12=0
x= -4
x/2 - 13 =8
x= 42
5(4x-11)=-75
x = -1
-5p + 1 = 6
p = -1
What is the Distributive Property?
The distributive property is where you multiply the number on the outside by each term on the inside.
12 fewer than 3 times a number is negative 29
3x-12=-29
5x-12=-80
x= -13.6
(x+2)/8 =-2
x= -18
-21 = 7(5k - 8)
k = 1
3(𝑥 − 9) = −3
x = 8
What rule is ALWAYS applied when solving equations?
Golden Rule of Algebra: What you do to one side, you do to the other side.
A fish tank has 180 gallons of water in it and is draining at a rate of 12 gallons per minute. After draining for a while, it now has 45 gallons in it. Write an equation to represent how many gallons of water are in the tub, and solve.
-12x+180=45
x=11.25 gallons