1. Solving Linear Equations

2. What is an equation? A statement in which 2 expressions are =
Ex: Which of the following are equations?
3x-7=12 b. 24x+5
2x-7x2+4x3 d. 12x+3= -4x-8

3. Properties of Equality
Addition prop of = - can add the same term to both sides of an equation.
Subtraction prop of = - can subtract the same term from both sides of an equation.
Multiplication prop of = - can multiply both sides of an equation by the same term.
Division prop of = - can divide both sides of an equation by the same term.
** So basically, whatever you do to one side of an equation, you MUST do to the other!

4. To solve an equation for a variable:
Do order of operations backwards (undo +/- first, then mult/div.)
Keep going until the variable is by itself on one side of the equation
You may have to simplify each side first.

5. Example: Solve for the variable.

6. Ex: Solve for x.

7. Ex: Solve the equations.
5(x-4)=5x+12
5x-20=5x+12
-20=12
Doesn’t make sense!
Answer: No solution
7x+14 -3x=4x+14
4x+14=4x+14
0=0
This one makes sense, but there’s no variable left!
Answer: All real numbers

8. Dry ice is solid CO2. It does not melt, but changes into a gas at -109
Dry ice is solid CO2. It does not melt, but changes into a gas at oF. What is this temperature in oC?

9. Examples Solve 11x-9y= -4 for y. Solve 7x-3y=8 for x. -11x -11x
-9y=-11x-4
Solve 7x-3y=8 for x.
+3y +3y
7x=3y+8

10. Ex: Solve the area of a trapezoid formula for b1.
A = ½ (b1+b2) h
2A = (b1+b2) h

11. Last Example:
You are selling 2 types of hats: baseball hats & visors. Write an equation that represents total revenue.
Price of baseball cap
# of caps sold
# of visors sold
Total Revenue
Price of visor
R = p1B + p2V