Solving Linear Equations B3 What is an equation? • A statement in which 2 expressions are = Ex: Which of the following are equations? a.
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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
5x 2 42 x 7 x
5 x 10 8 x 28 x
2
x8
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