# Algebra by yurtgc548

VIEWS: 5 PAGES: 20

• pg 1
Algebra
The beginnings of a continual

How are equations solved using
Properties of Equality?
Inverse Operations
Inverse, or opposite, operations
– Multiply/Divide
– Square/square root
Inverse operations “undo” each
other.
Subtraction Property of Equality
If you subtract the same number
from each side of an equation, the
two sides remain equal.
x+2=3
-2 -2
x=1
If you add the same number to each
side of an equation, the two sides
remain equal.
x-2=4
+2 +2
x=6
Balancing Equations
The equal sign divides the equation
into 2 sides.
Both sides of the equation must
remain equal or balanced.
The Golden Rule of solving
equations: What you do to one side,
you MUST do to the other side.
Examples
x-2=1          x+4=9
+2 +2           -4 -4
x=3             x=5
Check: 3-2=1   Check: 5+4=9
1=1            9=9
Subtraction Equations
(a – f)
Be sure to check your solution.
Word Problem Example
Tiger Woods won the 2002 Masters
Championship with a final score of 12
under par, or -12. His scores for the first
three rounds were -2, -3, and -6. What
was his score for the fourth round?
(-2)+(-3)+(-6)+s=(-12)
Combine like terms
(-11)+s=(-12)
+11       +11
s=(-1)
He needs to score 1 under par for the 4th
round.
Summarizer
Suppose your friend was absent the day we
equations. Write a letter to your friend, in two
paragraphs, explaining how to solve the two
following equations:
62 = f – 14                 y + 12 = -3

The following words or phrases must be included
solve     -Subtraction Property of Equality
Inverse operation
balance
Solving Multiplication and
Division Equations
How are equations solved using
the Division and Multiplication
Properties of Equality?
Division Property of Equality
If you divide each side of an equation by the
same nonzero number, the two sides remain
equal.
2x= (-6)
2     2
x=(-3)
Check: 2(-3)=(-6)
-6 = -6

Word Problem Example
The tortoise is one of the slowest land
animals, reaching a top speed of about
0.25 mile per hour. At this speed, how
long will it take a tortoise to travel 1.5
miles?
Distance=rate * time
1.5=0.25t

At this speed, it would take a tortoise ___
hours to travel 1.5 miles.
Solving Division Equations

What is the opposite of division?
Multiplication Property of Equality:
If you multiply each side of an equation by the
same number, the two sides remain equal.
a = -7                To Check:
-3                        a = 21
-3 * a = -7 * -3             21 = -7
1 -3                        -3
a = 21                   -7 = -7

Your Turn P. 51 (d – f).
Summarizer

Keeping in mind what you have reviewed
today, consider the following equation:
10x – 2 = 28.

Create a flow map demonstrating how to
solve this two-step equation. Place the
equation in the first square then place one
step in each square. The final square
should contain the solution.
The Next Step
Now that you know how to solve
one-step equations…
You will combine this knowledge to
solve two-step equations
Two Step Equations
A problem with two different
operations
backwards to solve—”Undo” the
order of operations
Compare
What you KNOW    NEW STUFF
2(3)+4           2x+4=10
6+4              2x+4=10
2nd: “undo” Multiply
2x=6
/2 /2
x=3
Analogy
to interview the man        1st: get rid of child
of the house alone          – 2x-3=1
1st: Get rid of the child   – +3 +3
– the addition or           – 2x=4
subtraction part of the   2nd: get rid of spouse
problem
– 2x=4
2nd:Get rid of the          – /2 /2
spouse                      – x=2
– the multiplication or
division part of the      Answer: x=2
problem