Introduction to Algebra

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```					ONE STEP
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.
ONE STEP EQUATIONS

To solve one step equations, you need
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 2 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
Using the addition property of equality, add 7 to both sides of
the equation.

thing on both sides to keep the equation equal.

y - 7 = -13
+7 +7
y = -6
ONE STEP EQUATIONS

Example 3 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 4 Solve b = -10
What is the variable?
2 The variable is b.
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

Solve the following
equations with one step
1. r + 4 = 17
2. g - 15 = -11
3. 13 + p = - 9
4. -5b = 85
5. - 7v = - 91
6. w = -2
3

1.   r = 13
2.   g = 4
3.   p = - 22
4.   b = - 17
5.   v = 13
6.   w=-6
Word Problems
with One Step Equations

You will need to know how to solve word problems involving
these equations, by using the four-step problem solving
plan:
2. Plan the solution
3. Solve the problem
4. Examine the solution
1. Explore the problem

problem
carefully, then:
• Identify what
information is
given
• Identify what you
2. Plan the Solution

• Choose a variable to represent the unknown that
you are trying to solve for
• Create an algebraic equation for solving
3. Solve the Problem 4. Examine the
Solution

• use algebraic
methods
“reasonable” ?

•   Did you check your
work to be sure?
Try it !

Write an Equation and Solve the Problem:
some athletic shoes for \$112, he had \$96 left.
How much was his paycheck?
• Let p = paycheck
• p - 112     =     96
•    + 112        +112
• p           =    208
• Noah’s paycheck was \$208.

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