Transcript 1.3 Solving Linear Equations

1.3 Solving Linear Equations
p. 19
What is an equation?
•
A statement in which 2 expressions are =
Ex: Which of the following are equations?
a. 3x-7=12
b. 24x+5
c. 2x-7x2+4x3
d. 12x+3= -4x-8
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!
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.
Example: Solve for the variable.
2
x  8  16
9
5x  2  42x  7  x
5x 10  8x  28  x
2
x 8
9
5x 10  7 x  28
9
x  8 
2
12x  18
12x 10  28
x
x  36
18
12
3
x
2
Ex: Solve for x.
2
1
3
x   2x 
3
5
10
1
3 
2

30 x    30 2 x  
5
10 
3

20x  6  60x  9
 40x  6  9
 40x  15
 15
x
 40
3
x 
8
Ex: Solve the equations.
5(x-4)=5x+12
5x-20=5x+12
-20=12
7x+14 -3x=4x+14
4x+14=4x+14
0=0
Doesn’t make sense!
Answer: No solution
This one makes sense,
but there’s no variable
left!
Answer: All real numbers
Dry ice is solid CO2. It does not melt, but
changes into a gas at -109.3oF. What is
this temperature in oC?
9
Use F  C  32
5
9
 109.3  C  32
5
9
 141.3  C
5
5
( 141.3)  C
9
 78.5o  C
1.4 Rewriting Equations &
Formulas
p. 26
Examples
• Solve 11x-9y= -4 for y.
-11x
-11x
-9y=-11x-4
-9
-9 -9
11 4
y  x
9 9
• Solve 7x-3y=8 for x.
+3y +3y
7x=3y+8
7 7 7
3
8
x y
7
7
Turn to page 28 in your
book.
Know the Common
Formulas Chart on this
page!
Ex: Solve the area of a trapezoid
formula for b1.
A = ½ (b1+b2) h
2A = (b1+b2) h
2A
 b1  b2
h
2A
 b2  b1
h
Last Example:
• You are selling 2 types of hats: baseball hats &
visors. Write an equation that represents total
revenue.
Total
Revenue
Price of
baseball
cap
# of
caps
sold
R = p1B + p2V
Price of
visor
# of
visors
sold
Assignment