Algebra by yurtgc548


 The beginnings of a continual
       math adventure.

How are equations solved using
 the Subtraction and Addition
    Properties of Equality?
      Inverse Operations
Inverse, or opposite, operations
– Add/Subtract
– Multiply/Divide
– Square/square root
Inverse operations “undo” each
Subtraction Property of Equality
 If you subtract the same number
 from each side of an equation, the
 two sides remain equal.
   -2 -2
Addition Property of Equality
If you add the same number to each
side of an equation, the two sides
remain equal.
 +2 +2
     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.
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
 Your Turn to Practice:
 Solving Addition and
 Subtraction Equations
       P. 46 Your Turn
            (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?
Combine like terms
+11       +11
He needs to score 1 under par for the 4th
Suppose your friend was absent the day we
reviewed solving addition and subtraction
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
in your paragraph:
solve     -Subtraction Property of Equality
Inverse operation
Addition Property of Equality
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
2x= (-6)
 2     2
Check: 2(-3)=(-6)
           -6 = -6

Your Turn P. 50 (a-c)
    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
Distance=rate * time

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).

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
Follow the order of operations
backwards to solve—”Undo” the
order of operations
What you KNOW    NEW STUFF
2(3)+4           2x+4=10
1st: Multiply    1st: “undo” Add
6+4              2x+4=10
2nd: Add            -4 -4
Answer: 10       2x=6
                 2nd: “undo” Multiply
                 /2 /2
Think about wanting         2x-3=1
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
                            – 2x=4
2nd:Get rid of the          – /2 /2
spouse                      – x=2
– the multiplication or
  division part of the      Answer: x=2
          Your Turn
Answer: x=2
Answer: n=-5
Answer: y=-2
More Practice
Workbook page 28

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