Transcript 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
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
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.