Solving one step equations
Properties of Equality
1.
Addition: If a = b then a + c = b + c.
2. Subtraction: If a = b then a – c = b– c.
3. Multiplication: If a = b then ac = bc.
4. Division: If a = b and c ≠ 0 then a/c = b/c
Rules to Remember
Quick Facts and
Definitions:



When solving an equation,
the goal is to get the
variable by itself on one
side of the equation.
Addition and subtraction
are inverse operations.
(opposites)
Multiplication and
division are inverse
operations. (opposites)
Solving Equations Requires
BALANCE!
Your equals sign will be
the fulcrum (balancing
point)!
Just remember, whatever
you do to one side must
be done to the other side
to maintain
balance……..
Addition / Subtraction


If the number to move is positive, subtract it from
both sides of the equation.
If the number to move is negative, add its positive
value to both sides of the equation.
Solving with Addition
Solve the following equation for x:
x – 4 =
9
+4
+4
x
=
13
We are able to get the x by itself
by ADDING 4 to each side!
(you WILL show this step in your homework!!)
Solving with Subtraction
Solve the following equation for p:
p + 7 =
21
-7
-7
p
=
14
We are able to get the p by itself
by SUBTRACTING 7 from each side!
(you WILL show this step in your homework!!)
Solving with Division
Solve the following equation for m:
3m =
18



Divide both sides by 3 and simplify -- your work should
look like this
:
3m =
3
m =
18
3
6
(you WILL show this step in your homework!!)
Solving with Multiplication
Problems involving fractions are solved using
multiplication, and the knowledge of multiplicative
inverses (reciprocals)
Example :
Solve the following equation for n:



2n
=
3
5
7
Multiply each side by the inverse of 25 :
5 • 2n
2
5
=
n
=
3 • 5
7
2
15
14
Your Turn:
Solve the following equations
with one step (show your
work!!):
1.
r + 4 = 17
2.
g - 15 = -11
3.
13 + p = - 9
4.
-5b = 85
5.
- 7v = - 91
6.
w = -2
3
9
Answers:
1.
2.
3.
4.
5.
6.
r = 13
g = 4
p = - 22
b = - 17
v = 13
w = - 2/3
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:
1.
Explore the problem
2.
Plan the solution
3.
Solve the problem
4.
Examine the solution
1. Explore the problem


First, read the
problem carefully,
then:
Identify what
information is
given
Identify what you
are asked to find
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

Is your answer
“reasonable” ?
Show your work!

Did you check your
work to be sure?

Let’s try it!
Read the following:
One mile is equal to approximately 1.6 kilometers. A
local running club is holding a 10 kilometer race.
What is the length of the race in miles?





Define aVariable Let m = the number of miles
1.6 • m = 10
Divide both sides by 1.6 (calculators ok)
m = 6.25
The length of the race is 6.25 miles.
One more !
Write an Equation and Solve the Problem:
Noah received a paycheck on Friday. After buying
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.
Homework:
You MUST show your work to get
credit on this assignment!!!