1' Simplify each side

1
SOLVING EQUATIONS WITH VARIABLES ON BOTH SIDES
1. Simplify each side
Get rid of parentheses, add like terms, etc.
2. Get rid of variable on right side
Add or subtract or use symmetric property.
3. Solve two step equation
Add or subtract then multiply or divide.
2
SOLVING EQUATIONS WITH VARIABLES ON BOTH SIDES
EXAMPLE
5x 3 3x 7
GET RID OF THE VARIABLE ON THE RIGHT SIDE
-3x -3x
2x 3 7
SOLVE 2-STEP EQUATION
3 3
2x 10
check 5(5) 3 3(5) 7
2 2
25 3 15 7
22 22
x 5
?
3
SOLVING EQUATIONS WITH VARIABLES ON BOTH SIDES
EXAMPLE
7 7(x 3)
SIMPLIFY BOTH SIDES
GET RID OF THE VARIABLE ON THE RIGHT SIDE
7 7x 21
7x 21 7
SYMMETRIC PROPERTY
SOLVE 2-STEP EQUATION
21 21
7x 28
check 7 7(4 3)
7 7
7 7(1)
7 7
x 4
?
4
SOLVING EQUATIONS WITH VARIABLES ON BOTH SIDES
EXAMPLE
2(m 3) 5 3(m 1)
SIMPLIFY BOTH SIDES
2m 1 3m - 3
GET RID OF THE VARIABLE ON THE RIGHT SIDE
-3m -3m
-m 1 -3
SOLVE 2-STEP EQUATION
1 1
check
-m -2
2(2 3) 5 3(2 1)
-1 -1
-2 5 3
?
m 2
5
RATIOS PROPORTIONS
A RATIO is a comparison of two numbers by
division.
Using the diagram at right, what is the ratio of
spades to clubs?
?
?
?
?
?
?
or 5/3
or 5 to 3
53
?
?
6
RATIOS PROPORTIONS
A RATIO is a comparison of two numbers by
division.
In a recipe, if you are to use 2 cups of flour
and 1 teaspoon of baking soda. What is the ratio
of flour to baking soda?
2 cups1 tsp
Units must be included
7
RATIOS PROPORTIONS
A RATIO is a comparison of two numbers by
division.
If Warren can read 120 pages in two days, what is
the ratio of pages read to days.
60 pages1 day
The ratio of two measurements having different
measures is called a RATE.
8
RATIOS PROPORTIONS
Other examples of rates.
200 miles in 4 hours
50 miles/hour
5.20 for 24 eggs
2.60 / dozen
48 for 15 gallons of gas
3.20 / gallon
9
RATIOS PROPORTIONS
A PROPORTION is an equation stating that two
ratios are equal.
means
extremes
In a proportion, the product of the means is
equal to the product of the extremes.
10
RATIOS PROPORTIONS
How do we know it is a proportion?
Cross Multiply (Means Extremes)
20
20
Yes, it is a proportion!
11
RATIOS PROPORTIONS
How do we know it is a proportion?
Cross Multiply (Means Extremes)
39
40
No, it is not a proportion!
12
RATIOS PROPORTIONS
Solving a proportion
Cross Multiply (Means Extremes)
2x
21
2x 21
x 21/2
13
RATIOS PROPORTIONS
Solving a proportion
Cross Multiply (Means Extremes)
15
2x - 4
2x - 4 15
2x 19
x 19/2
14
PROBLEM SOLVING USING PROPORTIONS
If Jenny can travel 520 miles in 9 hours, how far
can she travel in 15 hours?
x distance traveled in 15 hours
9x
7800
9x 7800
x 866.7 miles
866.7 miles
15
PROBLEM SOLVING USING PROPORTIONS
If Al can read 1240 words in 3 minutes, how many
words can he read in 20 minutes?
x words read in 20 minutes
3x
24800
3x 24800
x 8266.7 words
8266.7 words
16
PRACTICE Variables on both sides
Solve 3(x 2) 4(x 5) 2
3x 6 4x 20 2
3x 6 4x 18
-4x -4x
-x 6 -18
-6 -6
-x -24
x 24
17
PRACTICE Ratios Proportions
Solve
4x 20 3x - 6
Cross Multiply
-3x -3x
x 20 -6
-20 -20
x -26