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1. Simplify each side
SOLVING EQUATIONS WITHVARIABLES ON BOTH SIDES
2. Get rid of variable on right side
3. Solve two step equation
Get rid of parentheses, add like terms, etc.
Add or subtract or use symmetric property.
Add or subtract; then multiply or divide.
EXAMPLE
5x – 3 = 3x + 7-3x -3x
2x – 3 = 7
GET RID OF THE VARIABLE ON THE RIGHT SIDE
SOLVING EQUATIONS WITHVARIABLES ON BOTH SIDES
+3 +32x = 102 2
x = 5
SOLVE 2-STEP EQUATION
check: 5(5) – 3 = 3(5) + 7
25 – 3 = 15 + 722 = 22☺
EXAMPLE
7 = 7(x – 3)
7x – 21 = 7
GET RID OF THE VARIABLE ON THE RIGHT SIDE
SOLVING EQUATIONS WITHVARIABLES ON BOTH SIDES
+21 +21
7x = 287 7
x = 4
SOLVE 2-STEP EQUATION
SIMPLIFY BOTH SIDES
7 = 7x – 21
SYMMETRIC PROPERTY
check: 7 = 7(4 – 3)
7 = 7(1)7 = 7
☺
EXAMPLE
2(m – 3) + 5 = 3(m – 1)
-m – 1 = -3
GET RID OF THE VARIABLE ON THE RIGHT SIDE
SOLVING EQUATIONS WITHVARIABLES ON BOTH SIDES
+1 +1
-m = -2-1 -1
m = 2
SOLVE 2-STEP EQUATION
SIMPLIFY BOTH SIDES
2m – 1 = 3m - 3-3m -3m
check
2(2 – 3) + 5 = 3(2 – 1)-2 + 5 = 3
☺
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?
5:3 or 5/3 or 5 to 3
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 cups:1 tspUnits must be included
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 pages:1 day
The ratio of two measurements having different measures is called a RATE.
RATIOS & PROPORTIONS
Other examples of rates.
200 miles in 4 hours50 miles/hour
$5.20 for 24 eggs
$2.60 / dozen
$48 for 15 gallons of gas$3.20 / gallon
RATIOS & PROPORTIONS
A PROPORTION is an equation stating that two ratios are equal.
4
10
2
5
extremesmeans
In a proportion, the product of the means is equal to the product of the extremes.
RATIOS & PROPORTIONS
How do we know it is a proportion?
4
10
2
5
Cross Multiply (Means = Extremes)
2020
Yes, it is a proportion!
RATIOS & PROPORTIONS
How do we know it is a proportion?
13
5
8
3
Cross Multiply (Means = Extremes)
3940
No, it is not a proportion!
RATIOS & PROPORTIONS
Solving a proportion
2
7
3x
Cross Multiply (Means = Extremes)
2x212x = 21x = 21/2
RATIOS & PROPORTIONS
Solving a proportion
2
3
5
2
xCross Multiply (Means = Extremes)
2x - 415
2x - 4 = 152x = 19x = 19/2
PROBLEM SOLVING USING PROPORTIONS
9
520
15
x
If Jenny can travel 520 miles in 9 hours, how far can she travel in 15 hours?
9x78009x = 7800
x = 866.7 miles
866.7 miles
x = distance traveled in 15 hours
PROBLEM SOLVING USING PROPORTIONS
3
1240
20
x
If Al can read 1240 words in 3 minutes, how many words can he read in 20 minutes?
3x248003x = 24800
x = 8266.7 words
8266.7 words
x = words read in 20 minutes
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
PRACTICE – Ratios & Proportions
Solve:
4x + 20 = 3x - 6-3x -3x
x + 20 = -6-20 -20
x = -26
4
2
3
5
xx
Cross Multiply
