Download 3.2-3.3 Solving Equations

3.2-3.3/6.1-6.2
Solving Equations/ Inequalities
ESSENTIAL PROPERTY OF
EQUATIONS/INEQUALITIES
:
Whatever you do to one side, you
must do to the other.
How do we know what one step
operation to perform?
Every operation has an
opposite operation to “undo”
it
ORIGINAL
OPERATION
ADDITION
SUBTRACTION
EQUATION
x+5 = 2
“UNDOING” OPERATION
Subtraction
x -5 = 2
Addition
MULTIPLICATION
5x = 2
Division
DIVISION
x=2
5
Multiplication
SOLUTION
x = -3
x =7
2
x
5
x=10
SOLVING :
Find all values for the variable that make
the equation/inequality true
identify what operation is being used with
the variable, and what partner operation will
undo it.
keep track of negative signs
Examples:
g + 3/4 = -1/8
A number increased by 5 is equal to 42.
SOLVING AN INEQUALITY USING
ADDITION AND SUBTRACTION:
 The rules for solving an EQUATION
and an INEQUALITY when you are
adding or subtracting are the SAME.
t – 45  13
7<x–4
12 + r ≥ 3
14 > t + 11
Examples:
t
7

30 10
(2 ¼)g = 1 ½
The weight of anything on the moon is about
one-sixth its weight on Earth. If an
astronaut’s suit weighs 33 pounds on the
moon, how much does it weigh on the Earth?
Examples:
The original Great Wall of China was 1000
miles long. In the fourteenth century, the
wall had to be repaired and was extended.
Today the wall is 2500 miles long. How
much of the wall was added during the
1300s?
Example 7&8:
Negative eighteen times a number equals –
198.
The rectangle is divided into 5 identical
squares. If the perimeter of the rectangle is
48, what is the area of each square?
SOLVING AN INEQUALITY USING
MULTIPLICATION & DIVISION:
inequality
 The rules for solving an _______________
when you are multiplying or dividing is
only different, when you are using a
________
negative number
________________________.
flipped/switched
The inequality sign must be __________________
when you multiply or divide by a negative
Solve the following one step
inequalities.
4 x  24
5 x  75
 3x  15

x
5
8
s
 12
7
2
x  4
7
1
x  2
5
r
 4
9
Translate and Solve the
Inequality:
The sum of a number and 13 is at least 27.
33 is greater than the difference of a number
and 5.
5 less than a number is greater than 20.
2 more than a number is less than -5.
Translate and Solve the
Inequality:
Sixteen is no more than two times a
number
Negative 7 times y is at least 14.
One-fourth of a number is less than –7.
Two-thirds a number is more than -12.