Download Addition Property of Equality

Algebra
3-2
3-3
3-4
SOLVING EQUATIONS BY USING ADDITION AND SUBTRACTION
SOLVING EQUATIONS BY USING MULTIPLICATION AND SUBTRACTION
SOLVING MULTI-STEP EQUATIONS
Warm-Up
Squares Partner Practice on Single-Step Equations
Definition: A solution is a value of a variable that makes a mathematical statement true.
The Goal:
To solve the equation for the given variable.
The First Rule:
JUST
SAY NO TO DOUBLE SIGNS!!
These are so confusing and lead only to problems. (What is that woman talking about?)
b + -7 = 11
x - -18 = 9
The Second Rule:
USE
y - +6 = 10
m + + 1 = -11
THE INVERSE OPERATIONS!!
What does that mean? If there is subtraction, undo it with addition. If there is
multiplication, undo it with division!! Here are the properties that let you do that.
PROPERTY
ADDITION PROPERTY
OF
SUBTRACTION PROPERTY
OF
MULTIPLICATION PROPERTY
DIVISION PROPERTY
MCD/LPG/MPH 10/12
EQUALITY
OF
EQUALITY
OF
EQUALITY
EQUALITY
SYMBOLICALLY
For any numbers a, b, and c, if a = b,
then a + c = b + c.
For any numbers a, b, and c, if a = b,
then a - c = b - c.
For any numbers a, b, and c, if a = b,
then ac = bc.
For any numbers a, b, and c and c  0,
if a = b, then
a
c
=
b
c
.
1
Algebra
Example 1
Solve each of the following single-step equations for the variable shown.
Be sure to rewrite the equation in the appropriate manner before solving.
1)
b + -7 = 11
2)
x - -18 = 9
3)
y - +6 = 10
4)
m + + 1 = -11
MULTI-STEP EQUATIONS
Definition:
A multi-step equation is an equation whose solution requires more than one
operation.
To solve a multi-step equation you usually…….
Step 1:
Simplify, simplify, simplify!! Simply both sides of the equation if possible.
Step 2:
Undo any addition or subtraction.
Step 3:
Undo any multiplication or division.
Example 2
Solve 4x – 3 = 11
MCD/LPG/MPH 10/12
2
Algebra
Example 3
1)
3)
5)
7)
Solve each of the following equations for the variable shown.
-5x + 3 = -12
2
7
x = -4
-11 -
x-1
5
a
3
= -8
= -2
MCD/LPG/MPH 10/12
n
=5
-3
2)
-17 +
4)
2 – n = -19
6)
8)
x-1
5
3
-4
= -2
x = -5
3
Algebra
3-2
3-3
3-4
SOLVING EQUATIONS BY USING ADDITION AND SUBTRACTION
SOLVING EQUATIONS BY USING MULTIPLICATION AND SUBTRACTION
SOLVING MULTI-STEP EQUATIONS
STRATEGIES
FOR
SOLVING WORD PROBLEMS
1)
Read the problem.
2)
Declare the variable:
3)
Write an equation representing the problem.
4)
Solve the equation.
5)
Check the answer.
6)
Write the answer in _____________________________________________
Examples
1)
____________________________________________
Solve each of the following word problems.
Six less than a number is -14. Find
the number.
LET
MCD/LPG/MPH 10/12
2)
Archie’s age increased by 16 is 62.
How old is Archie?
LET
4
Algebra
3)
The product of
3
and a number is
4)
Five more than the quotient of a
number and -6 is 8. What is the
number?
6)
Henry’s age divided by 5, the result
decreased by 11 is 7. How old is
Henry?
4
-15. Find the number.
LET
5)
Twice the cost of a shirt increased by
$23 is $67. What is the cost of the
shirt?
MCD/LPG/MPH 10/12
5
Algebra
3-2
3-3
3-4
SOLVING EQUATIONS BY USING ADDITION AND SUBTRACTION
SOLVING EQUATIONS BY USING MULTIPLICATION AND SUBTRACTION
SOLVING MULTI-STEP EQUATIONS
Warm-Up
1)
Solve each of the following word problems.
The quotient of a number and -11
increased by 16 is -4. Find the
number.
MCD/LPG/MPH 10/12
2)
Eight less than three times Max’s quiz
grade is 241. What is his grade?
6