Transcript Solving Equations PowerPoint

Solve Equations With
Variables on Both Sides
Steps to Solve Equations
with Variables on Both Sides
 1)
Get rid of ( ) on both sides of
equation.
 2) Combine like terms on both sides.
 3) Get variable on one side of the
equation
 4) Solve 2 step equation by undoing
what has been done to the variable.
Use Steps to Solve Equation:
2(x + 7) + 3 = 5x - 1
2x + 14 + 3 = 5x – 1
2x + 17 = 5x - 1
-5x
-5x
-3x + 17 = - 1
- 17 - 17
-3x = -18
-3
-3
x= 6
1) Get rid of ( ) --distribute
2) Combine like terms
3) Get variables on same
side – use inverse operation
4) Solve 2 step equation
Undo by using inverse
 -3
 -3 undo 2nd
+ 17
- 17
undo 1st
Check - replace “x” with solution
2(x + 7) + 3 = 5x - 1
2(6 + 7) + 3 =5(6) - 1
2(13) + 3 =5(6) - 1
26 + 3 = 30 - 1
29 = 29

X=6
1) Replace X = 6
2) Follow order of
operations on both
sides of equation
3) Checks
is the solution
to the equation
Use Steps to Solve Equation:
-3x + 4 = 5x – 8
-5x
-5x
-8x + 4 = - 8
-4 -4
-8x = -12
-8
-8
x = 1.5
Get variables on same side
of equation – use inverse
operation (subtract 5x)
Solve 2 step equation
Undo by using inverse
 -8
 -8 undo 2nd
+4
-4
undo 1st
Use Steps to Solve Equation:
4(1 – 2x) = 4 – 6x
4 – 8x = 4 - 6x
+6x
+ 6x
4 - 2x = 4
-4
-4
-2x = 0
-2 -2
x= 0
Get rid of ( ) -- distribute
Get variables on same side
– use inverse operation
(add 6x)
Solve 2 step equation
Undo by using inverse
 -2
 -2 undo 2nd
+4
-4
undo 1st
Use Steps to Solve Equation:
9 + 5x = 5x + 9
-5x -5x
9=9
x = any real
number
Get variables on same side
of equation – use inverse
operation (subtract 5x)
The variables zeroed out
and remaining is a true
statement where a
number is equal to itself –
this is called an identity
The solution is all real
numbers
Use Steps to Solve Equation:
6x – 1 = 6x – 8
-6x
-6x
-1 = - 8
x = no solutions
The solution is no real
numbers or empty set
Get variables on same side
of equation – use inverse
operation (subtract 6x)
The variables zeroed out
and remaining is a false
statement where a
number is equal to a
different number, so there
will be no number that will
work in the equation.
Review Steps to Solve Equations
with Variables on Both Sides
 1)
Get rid of ( ) on both sides of
equation.
 2) Combine like terms on both sides.
 3) Get variable on one side of the
equation.
 4) Solve 2 step equation by undoing
what has been done to the variable.
 5) Remember 2 special cases when the
variable zeros out.
The end