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Transcript
Algebra 1/2
Section 2.5 Solving Multi-step
equations with variables on both sides
Monday, September 12th
Example 1: Solving Equations with Variable on both
sides
 Step 1: Use the Addition
or Subtraction Property
of Equality to write an
equivalent equation with
all the variables on one
side
x – 6 = –2x + 3
x +2x -6 = –2x +2x + 3
3x – 6 = 3
3x – 6 + 6 = 3 + 6
 Step 2:Use the
Multiplication or Division
Property of Equality to
solve.
Original Equation
Add 2x to both sides
Simplify
Add 6 to both sides
3x = 9
Simplify
3x = 9
3
3
Divide both sides by
3 to isolate the
variable.
x=3
Example 2: Solving Equations with grouping symbols.
 Step 1: Simplify the
expression on each
side. Use the distributive
property as needed.
 Step 2: Use addition
and/or subtraction to get
all the variables on one
side of the equation and
the constant terms on
the other side.
4(2r – 8) = 1/7(49r+70)
8r - 32 = 7r + 10
8r - 7r - 32 = 7r - 7r + 10
1r - 32 = 10
Original Equation
Distribute
Subtract 7r from both
sides
Simplify
Add 32 to both sides
 Step 3: Use division or
multiplication to solve.
1r - 32 + 32 = 10 + 32
1r = 42
Simplify
Check: 4(2r – 8) = 1/7(49r+70) when r = 42.
4(2r – 8) = 1/7(49r+70)
Example 3: Solving Equations with no solution or identity.
New Vocabulary: Identity
2m + 5 = 5(m–7) -3m
Original
Equation
2m + 5 = 5m–35 -3m
Distribute
2m - 2m+ 5 = 2m -2m - 35
5 = -35
This statement is false,
There is no solution.
An equation that is true for all values of the
variables.
Subtract 2m
from both sides
3(r + 1) - 5 = 3r - 2
Original
Equation
3r + 3 - 5 = 3r - 2
Distribute
3r - 2 = 3r - 2
Simplify by
combining like
terms.
Simplify
Since the
Reflexive
expressions on each Property of
side of the equation Equality
are the same this is
an Identity.
Solve the equations:
a. 14 – 3y = 4y
b. 4x – 15 = 17 – 4x
Solve the equations:
c. 10x – 22 = 29 – 7x
d. r – 4 + 6r = 3 + 8r
Homework
Page 101 (11-43 odd, 49, 50)
This is different than your assignment
sheet so write it down.