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```					Math 060 WORKSHEET                                             NAME:_________________________
2.3 Solving Linear Equations
Consider the equation:
3x  5  13
We are undoing what is happening to x ( Multiplication by 3 and subtraction by 5 ) . So we undo by
going backwards: undo subtraction of 5 and then undo multiplication by 3.
3x  5  13
 __   ___
3x  ____
3x  _____
___ _____
x  ____
Any equation that can be written in the form ax  b  c is called a linear equation. In this section all of
the equations are linear. To solve linear equations:
1.) Simplify both sides of the equation.
2.) Collect all the variable terms and all constant terms on the other side.
3.) Isolate the variable and solve.

EXAMPLE: Solve and Check
a.)  4 p  3  2                    b.)  8  3c  2                     c.)  0.2  0.8  y

2x
To Solve         7 we can do two things:
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2x                                               2x                      3
___       ___ 7   multiply by 3          or    ___     ___ 7 multiply by
3                                               3                       2
2 x  ____           divide by 2                  x  ____
x  ___

EXAMPLE: Solve and Check
2
b  3  15
3

Sometimes it may be necessary to simplify before trying to solve. We get all the x' s together and the
constants together before we solve.

EXAMPLE: Solve and Check
a.)  5x  3  3x  11        b.) 8 y  4  4 y    c.) 42 x  1  29  32 x  5

1
Many people would love to do away with having to deal with fractions. When an equation has fractions
involved, we may use the multiplication property of equality to clear the fractions. We multiply both
sides by the LCD.
x 1       1                        EXAMPLE: Solve:
         LCD = 8
4 2       8                                      x 2x 5
                    LCD = _____
x 1      1                                      4 3 6
8    
4 2      8
x   1      1
8  8   8  
4 2        8
2x  4  1
2x  5
5
x
2
Therefore we don’t need to deal with
fractions very much.

IDENTITIES AND IMPOSSIBLE EQUATIONS:
The equations that we have been solving are called conditional equations because they only work
for one number. An equation that is true for all values of its variable is called an identity.
3x  2  3x  6 is an identity

2x  2  2x  3 is an equation that is never true.

Solve the above equation to see what happens:
3x  2  3x  6                                    2x  2  2x  3

EXAMPLE: Solve the equation.
2x  6
a.)  3s  2  2s  4  s                      b.) x  7           4
2

EXAMPLE: A driver left the plant with 300                                         W
bottles of drinking water on his truck. His route      EXAMPLE: The formula:         3H  53 models the
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consisted of office buildings, each of which           recommended weight, W , in pounds, for a male,
received 3 bottles of water. The driver returned       where H represents the man’s height , in inches,
to the plant with 117 bottles on the truck. To         over 5 feet. What is the recommended weight for a
how many office buildings did he deliver?              man who is 6 feet, 3 inches tall?

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