Transcript Solving Linear Equations B3 What is an equation? • A statement in which 2 expressions are = Ex: Which of the following are equations? a.

Solving Linear Equations
B3
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2 x  7  x
5 x  10  8 x  28  x
2
x8
9
5 x  10  7 x  28
9
x  8 
 2
12 x  18
x  36
12 x  10  28
x
18
12
x
3
2
Ex: Solve for x.
2
1
3
x   2x 
3
5
10
1
3
2

30 x    30 2 x  
5
10 
3

20 x  6  60 x  9
 40 x  6  9
 40 x  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
 78.5  C
o