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
GET RID OF THE VARIABLE ON THE RIGHT SIDE
5x – 3 = 3x + 7
-3x x
2x – 3 = 7
SOLVE 2-STEP EQUATION
2x = 10
check: 5(5) – 3 = 3(5) + 7
25 – 3 =
22 = 22
x = 5 ☺

3. ☺ SOLVING EQUATIONS WITH VARIABLES ON BOTH SIDES EXAMPLE 7 = 7(x – 3)
SIMPLIFY BOTH SIDES
7 = 7(x – 3)
GET RID OF THE VARIABLE ON THE RIGHT SIDE
7 = 7x – 21
7x – 21 = 7
SYMMETRIC PROPERTY
SOLVE 2-STEP EQUATION
7x = 28
check: 7 = 7(4 – 3)
7 = 7(1)
7 = 7
x = 4 ☺

4. ☺ SOLVING EQUATIONS WITH VARIABLES ON BOTH SIDES EXAMPLE
SIMPLIFY BOTH SIDES
2(m – 3) + 5 = 3(m – 1)
2m – 1 = 3m - 3
GET RID OF THE VARIABLE ON THE RIGHT SIDE
-3m m
-m – 1 = -3
SOLVE 2-STEP EQUATION
check
-m = -2
2(2 – 3) + 5 = 3(2 – 1)
= 3 ☺
m = 2

5. ♠ ♣ ♠ ♣ ♠ ♣ ♠ ♠ A RATIO is a comparison of two numbers by division.
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 to 3 ♠ ♠

6. A RATIO is a comparison of two numbers by division.
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 tsp
Units must be included

7. A RATIO is a comparison of two numbers by division.
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.

8. Other examples of rates.
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. A PROPORTION is an equation stating that two ratios are equal.
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. How do we know it is a proportion?
RATIOS & PROPORTIONS
How do we know it is a proportion?
Cross Multiply (Means = Extremes) 20 20
Yes, it is a proportion!

11. How do we know it is a proportion?
RATIOS & PROPORTIONS
How do we know it is a proportion?
Cross Multiply (Means = Extremes) 40 39
No, it is not a proportion!

12. Cross Multiply (Means = Extremes)
RATIOS & PROPORTIONS
Solving a proportion
Cross Multiply (Means = Extremes) 21 2x
2x = 21
x = 21/2

13. Cross Multiply (Means = Extremes)
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
7800 9x
9x = 7800
x = 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 = words
words

16. PRACTICE – Variables on both sides
Solve: 3(x + 2) = 4(x – 5) + 2
3x + 6 = 4x –
3x + 6 = 4x – 18
-4x x
-x + 6 = -18
-x = -24
x = 24

17. PRACTICE – Ratios & Proportions
Solve:
Cross Multiply
4x + 20 = 3x - 6
-3x x
x + 20 = -6
x = -26