Transcript Solving Two-Step Equations - C on T ech Math : : An application

Solving Two-Step Equations
Tutorial 6b
Solving Two-Step Equations
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A two-step equation is an equation that
has two operations.
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The following equations are one-step
equations:
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y + 2 = 12 or 5x = 40 or a/4 = 10.
These are two-step equations:

2x + 5 = 11 or 12r – 7 = 17 or y/8 + 6 = 10
Solving Two-Step Equations
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One way to solve an equation is to get the
variable alone on one side of the equal sign.
You can do this by using inverse operations,
which are operations that undo one another.
Solving Two-Step Equations
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Addition and subtraction are inverse
operations.
You can use subtraction to undo addition
and addition to undo subtraction .
Multiplication and division are inverse
operations.
You can use division to undo multiplication
and multiplication to undo division.
Example #1
Suppose you earn $4 per hour baby-sitting and pay $1 in bus fare
each way. You want to buy a T-shirt that costs $10. To find the
number of hours you must work to buy the T-shirt, solve the equation
4x – 2 = 10.
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Think to yourself: What is being done to the variable (x)?
A 4 is being multiplied to the variable (x). And a 2 is being
subtracted from the term having the variable (x).
Division undoes multiplication and -- Addition undoes
subtraction.
This is a two-step equation because there are two operations
that must be undone.
Example #1
Suppose you earn $4 per hour baby-sitting and pay $1 in bus fare
each way. You want to buy a T-shirt that costs $10. To find the
number of hours you must work to buy the T-shirt, solve the equation
4x – 2 = 10.
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When solving a two-step equation - - always undo any
addition or subtraction first!
Then undo any multiplication or division.
Remember, whatever you do to one side of an equation
you must also do to the other side.
Example #1
Suppose you earn $4 per hour baby-sitting and pay $1 in bus fare
each way. You want to buy a T-shirt that costs $10. To find the
number of hours you must work to buy the T-shirt, solve the equation
4x – 2 = 10.
 To undo the subtraction, add a 2
4x – 2 = 10
to each side of the equation.
 To undo the multiplication, divide
by 4 on each side of the equation.
 x is now all alone on one side of
the equation!
You will have to work for 3 hours
in order to buy the T-shirt.
+2 +2
14x = 12 3
4
4 1
1
x = 3
Always check your answers!
4x - 2 = 10; Does x =3?
4•3 - 2 = 10 is true!
Example #2
Solve the Equation:
m
1  5
12
m
 To undo the addition, subtract a 5
1  5
12
from each side of the equation.
-5
-5
m
 To undo the division, multiply by
1

-12 on each side of the equation. (-12)• - 4 = 12 •(-12)
1
 x is now all alone on one side of
the equation!
48 = m
Always check your answers!
1 
m
 5; Does m  48?
12
1 
48
 5; is true!
12