Download Solving Equations

Solving Equations
Inverse Operations
 When solving equations algebraically,
use the inverse (opposite) operation that
is displayed to determine what value yhe
variable (letter) has.
Opposite (inverse)
operations:




Addition is the opposite of subtraction
Subtraction is the opposite of Addition
Multiplication is the opposite of Division
Division is the opposite of multiplication
Types of Equations:
 There are five types of equations.
 Type 1 (Adding)
Type 1 (subtracting)
X+6=8
X+6–6=8–6
X= 2
x–8=4
x–8+8=4+8
x = 12
Type 1 Equations
( Continued)
Type 1 ( Multiplying)
5x= - 35
5x = -35
5
5
X=-7
Type 1 (Division)
x = -8
3
x * 3 = -8 * 3
3
x = -24
Type 2 Equations
Type 2 (adding)
Type 2 (subtracting)
3x + 8 = 24
5x-3=12
3x + 8-8=24-8
3x= 16
3x= 16
3
3
X= 5 1/3
5x-3+3= 12+3
5x= 15
5x = 15
5
5
x= 3
Type 2 Equations
(continued)
Type 2 (Division)
X + 5 = - 1.2
8
X +5 - 5 = -1.2 - 5
8
X = -6.2
8
X * 8 = -6.2 * 8
8
X= - 49.6
Type 3 Equations
 A type 3 equation is one where there is more
than one group of variables. To solve a type 3
equation, collect and place all the variables on
the left of the equal sign, and all the constants
on the right of the equal sign.
Remember: When accomplishing this if a
constant or variable crosses over the equal
sign, change its sign to the opposite!!!!
Type 3 equations
(Continued)
5x-3=3x+14
7x – 3x= 44
5x-3x=14+3
2x=17
2x = 17
2
2
X=8.5
4x= 44
4x = 44
4
4
x=11
Type 4 Equations
A type 4 equation has one or more sets of
brackets. Use the number on the outside
of the bracket as a multiplier (distributive
property), and multiply it by everything in
the brackets. Once this is done, solve
the equation normally.
Type 4 equations
(Continued)
3(x+7)= - 39
3x + 21 = -39
3x + 21 – 21 = -39 – 21
3x = -60
3x = -60
3
3
X= -20
Another example (Type 4)
4(2X-5)=2(3X+6)
8X-20 = 6X+12
8X-6X = 12 + 20
2X = 32
2X = 32
2
2
X= 16
Ratio Type Equations
A ratio type equation is classified as one in
which there are two “fractions” on either
side of the equal sign.
Ratio type equations
(Continued)
X = -3
6 2
2(x) = 6(-3)
2x = -18
2x = -18
2
2
X= -9
A more complicated Ratio
type equation.
3x+5 = 7
4
2
2(3x+5) = 4(7)
6x+10 = 28
6x+10-10 = 28 – 10
6x= 18
6x = 18
6
6
X= 3