1. Solving Linear Equations
Chapter 2
Solving Linear Equations

2. 2.1 Writing Equations 4 Steps to Problem Solving
Explore the problem (read the whole thing)
Plan the solution (write the equation)
Solve the problem
Check the solution (does it make sense?)

3. How to use a Formula Perimeter=2l+2w Area of a Square= lw
Write the formula
Substitute for any known variables
Solve the equation
Check the answer (does it make sense?)
Perimeter=2l+2w
Area of a Square= lw
Area of a Triangle= ½ bh
Area of a Circle= r2

4. 2.2 Solving Equations by Using Addition and Subtraction
To solve an equation means to find all values of the variable that make it true
Addition Property of Equality:
If you add the same amount to each side of the equal sign, the equation is true
Ex: m – 48 = 29

5. Subtraction Property of Equality:
If you subtract the same amount from each side, the equation is true
42 + d = 27 n + 5 = 40

6. 2.3 Solving Equations by Using Multiplication and Division
Multiplication Property of Equality:
If you multiply each side of the equal sign by the same number, the equation is true
t/3 = /4g = 1/2

7. Division Property of Equality:
If you divide each side of the equal sign by the same number, the equation is true
13s = x = 36

8. 2.4 Solving Multi-Step Equations
Add or Subtract the number farthest from the variable
Multiply or divide the number next to the variable
Simplify
Check your answer

9. Examples:
(p – 15)/9 = /3y – 25 = 115

10. Even consecutive and odd consecutive numbers = x, x+2, x+4, x+6….
Find three consecutive integers whose sum is 21
Find three consecutive even integers whose sum is -42

11. 2.5 Solving Equations with Variables on Each Side
Distribute and/or combine like terms
Add or subtract the variables to one side (move the smaller one)
Add or subtract the numbers to the other side
Solve as normal

12. Examples:
k = 8k m = 5 = 5(m – 7) -3m

13. 2.6 Ratios and Proportions
Ratio: a comparison of two numbers by division
x to y x : y
ex: Your class has 21 students, 9 are boys and 12 are girls
a. ratio of boys to girls ________________
b. ratio of students to boys _____________
Scale: a ratio that shows that a model is proportional to an actual object

14. Proportion: shows that two ratios are equal
a and d are the extremes
b and c are the means
Solve a proportion by cross multiplying .
ad = bc

15. Ex: Determine if it is a proportion. Ex: Solve the proportion.b.

16. 2.7 Percent of Change New # is greater than original # = % of increase
New # is less than original # = % of decrease
To solve:

17. Original: $25
New: $28
Original: 16
New: 3

18. Concert tickets cost $45 each. The tax is 6. 25%
Concert tickets cost $45 each. The tax is 6.25%. What is the total cost for one ticket?
A sweater is on sale for 35% off. The original price is $38. What is the sale price?

19. 2.8 Solving for a Specific Variable
Use the normal order of operations and problem solving steps to get the specific variable on one side of the equal sign and everything else on the other side of the equal sign

20. Solve 3x – 4y = 7 for y.
Solve 2m – t = sm + 5 for m.

21. Solve C=2 r for r
Solve for a.

22. 2.9 Weighted Averages
Weighted average: the sum of a product of units and value per unit, divided by the sum of the # of units

23. How many pounds of mixed nuts selling for $4
How many pounds of mixed nuts selling for $4.75 per pound should be mixed with 10 pounds of dried fruit selling for $5.50 per pound, to obtain trail mix that sells for $4.95 per pound?
# Units
Price per Unit
Product
Dried Fruit 10
5.50
550
Nuts
4.75
Trail Mix
4.95 x
4.75x
10 + x
4.95(10 + x)
x = 4.95(10 + x)
SOLVE FOR X

24. An experiment calls for 30% solution of copper sulfate
An experiment calls for 30% solution of copper sulfate. Kendra has 40ml of 25% solution. How many ml of 60% solution should be added?
Amount/Units
Product
25% Solution
60% Solution
30% Solution 40
40 x .25= 10 x
.6x
40 + x
.3(40 + x)
x = .3(40 + x)
SOLVE FOR X