1. 2.1 The Addition Property of Equality
A linear equation in one variable can be written in the form: Ax + B = 0
Linear equations are solved by getting “x” by itself on one side of the equation
Addition Property of Equality: if A=B then A+C=B+C
General rule: Whatever you do to one side of the equation, you have to do the same thing to the other side.

2. 2.1 The Addition Property of Equality
Example of Addition Property: x – 5 = (add 5 to both sides) x = 17
Example using subtraction:

3. 2.2 The Multiplication Property of Equality
Multiplication Property of Equality: if A=B and C is non-zero, then AC=BC (both equations have the same solution set)
Since division is the same as multiplying by the reciprocal, you can also divide each side by a number.
General rule: Whatever you do to one side of the equation, you have to do the same thing to the other side.

4. 2.2 The Multiplication Property of Equality
Example of Multiplication Property:
Example using division 5x = (divide both sides by 5) x = 12

5. 2.3 More on Solving Linear Equations: Terms - Review
As with expressions, a mathematical equation is split up into terms by the +/-/= sign:
Remember, if the +/- sign is in parenthesis, it doesn’t count:

6. 2.3 More on Solving Linear Equations: Multiplying Both Sides by a Number
Multiply each term by the number (using the distributive property).
Within each term, multiply only one factor. Notice that the y+1 does not become 4y+4

7. 2.3 More on Solving Linear Equations: Clearing Fractions
Multiply both sides by the Least Common Denominator (in this case the LCD = 4):

8. 2.3 More on Solving Linear Equations: Clearing Decimals
Multiply both sides by the smallest power of 10 that gets rid of all the decimals

9. 2.3 More on Solving Linear Equations: Why Clear Fractions?
It makes the calculation simpler:

10. 2.3 More on Solving Linear Equations
1 – Multiply on both sides to get rid of fractions
2 – Use the distributive property to remove parenthesis
3 – Combine like terms
4 – Put variables on one side, numbers on the other by adding/subtracting on both sides
5 – Get “x” by itself on one side by multiplying both sides
6 – Check your answers

11. 2.3 More on Solving Linear Equations
Example:

12. 2.4 An Introduction to Applications for Linear Equations
1 – Decide what you are asked to find
2 – Write down any other pertinent information (use other variables, draw figures or diagrams )
3 – Translate the problem into an equation.
4 – Solve the equation.
5 – Answer the question posed.
6 – Check the solution.

13. 2.4 An Introduction to Applications for Linear Equations
Find the measure of an angle whose complement is 10 larger.
x is the degree measure of the angle.
90 – x is the degree measure of its complement
90 – x = 10 + x
Subtract 10: 80 – x = x Add x: 80 = 2x Divide by 2: x = 40
The measure of the angle is 40 
Check: 90 – 40 =

14. 2.5 Formulas - examples A = lw I = prt P = a + b + c d = rt V = LWH
C = 2r
Area of rectangle
Interest
Perimeter of triangle
Distance formula
Volume – rectangular solid
Circumference of circle

15. 2.5 Formulas
Example: d=rt; (d = 252, r = 45) then 252 = 45t divide both sides by 45:

16. 2.6 Ratios and Proportions
Ratio – quotient of two quantities with the same units Examples: a to b, a:b, or Note: percents are ratios where the second number is always 100:

17. 2.6 Ratios and Proportions
Proportion – statement that two ratios are equal Examples: Cross multiplication: if then

18. 2.6 Ratios and Proportions
Solve for x: Cross multiplication: so x = 63

19. 2.7 More about Problem Solving
Percents are ratios where the second number is always 100: Example: If 70% of the marbles in a bag containing 40 marbles are red, how many of the marbles are red?: #red marbles =

20. 2.7 More about Problem Solving
How many gallons of a 12% indicator solution must be mixed with a 20% indicator solution to get 10 gallons of a 14% solution? Let x= #gallons of 12% solution, then 10-x= #gallons of 20% solution :

21. 2.8 Solving Linear Inequalities
< means “is less than”
 means “is less than or equal to”
> means “is greater than”
 means “is greater than or equal to” note: the symbol always points to the smaller number

22. 2.8 Solving Linear Inequalities
A linear inequality in one variable can be written in the form: ax < b (a0)
Addition property of inequality: if a < b then a + c < b + c

23. 2.8 Solving Linear Inequalities
Multiplication property of inequality:
If c > 0 then a < b and ac < bc are equivalent
If c < 0 then a < b and ac > bc are equivalent note: the sign of the inequality is reversed when multiplying both sides by a negative number

24. 2.8 Solving Linear Inequalities
Example: -9