Transcript Alex Sowa One_Step_Equation

ONE STEP
EQUATIONS
Addition and Subtraction Equations
Multiplication and Division Equations
ONE STEP EQUATIONS
An equation is like a balance scale
because it shows that two
quantities are equal.
What you do to one side of the
equation must also be done to the
other side to keep it balanced.
Definitions
• Term: a number, variable or the product
or quotient of a number and a variable.
12
X
2w
c
3
• Terms are separated by addition (+) or
subtraction (-) signs.
• 3a – 2b + 7x – 4z + 52
5
How many Terms do you see?
5
Definitions
• Constant:
a term that is a number.
• Coefficient:
the number value in
front of a variable in a term.
3x – 6y + 18 = 0
3 , -6
What are your coefficients?
What is your constant?
18
ONE STEP EQUATIONS
To solve one step equations, you need
to ask three questions about the
equation:
• What is the variable?
• What operation is performed on the variable?
• What is the inverse operation?
(The one that will undo what is being
done to the variable)
ONE STEP EQUATIONS
Example 1 Solve x + 4 = 12
What is the variable? The variable is x.
What operation is being performed on the variable? Addition.
What is the inverse operation (the one that will undo what is
being done to the variable)?
Subtraction.
Using the subtraction property of equality, subtract 4 from both
sides of the equation.
The subtraction property of equality tells us to subtract
the same thing on both sides to keep the equation equal.
x + 4 = 12
-4
-4
x = 8
ONE STEP EQUATIONS
Example 1 Solve y - 7 = -13
What is the variable? The variable is y.
What operation is being performed on the variable? Subtraction.
What is the inverse operation (the one that will undo what is being
done to the variable)?
Addition.
Using the addition property of equality, add 7 to both sides of
the equation.
The addition property of equality tells us to add the same
thing on both sides to keep the equation equal.
y - 7 = -13
+7 +7
y = -6
ONE STEP EQUATIONS
Example 1 Solve –6a = 12
What is the variable? The variable is a.
What operation is being performed on the variable? Multiplication.
What is the inverse operation (the one that will undo what is being done
to the variable)?
Division
Using the division property of equality, divide both sides of the
equation by –6.
The division property of equality tells us to divide the same
thing on both sides to keep the equation equal.
–6a = 12
-6
-6
a = -2
ONE STEP EQUATIONS
Example 1 Solve b = -10
2 The variable is b.
What is the variable?
What operation is being performed on the variable? Division.
What is the inverse operation (the one that will undo what is
being done to the variable)?
Multiplication
Using the multiplication property of equality, multiply both sides
of the equation by 2.
The multiplication property of equality tells us to multiply
the same thing on both sides to keep the equation equal.
b
= -10
2
b
2 •
= -10 • 2
2
b = -20
• 1) 26 = 8 + v
• What is the variable? The variable is v.
• What operation is being performed on the variable? Addition.
• What is the inverse operation (the one that will undo what
is being done to the variable)?
Subtraction.
• Solve
26 = 8 + v
-8 -8
18 = v or v = 18
• 2) x - 7 = 13
• What is the variable? The variable is x.
• What operation is being performed on the variable? Subtraction.
• What is the inverse operation (the one that will undo what
is being done to the variable)? Addition.
• Solve
x – 7 = 13
+7 +7
x = 20
• 3) v / 8 = 2
• What is the variable? The variable is v.
• What operation is being performed on the variable? Division.
• What is the inverse operation (the one that will undo what
is being done to the variable)? Multiplication.
• Solve
8 • v=2 •8
8
v = 16
• 4) -126 = 14k
• What is the variable? The variable is k.
• What operation is being performed on the variable? Multiplication.
• What is the inverse operation (the one that will undo what
is being done to the variable)? Division.
• Solve
-126
____= 14k
___
14
14
-9 = k or
k = -9
Works Cited
• Charles, Randall I., Bonnie McNemar, and Alma
Ramirez. Pre-algebra. Boston, Massachusetts:
Pearson Prentice Hall, 2007. Print.
• Free Algebra 1 Worksheets. (n.d.). Create Custom
Pre-Algebra, Algebra 1, Algebra 2, and Geometry
Worksheets. Retrieved October 17, 2011, from
http://www.kutasoftware.com/free.html