3-5 Solving Equations with the
variable on each side
Objective: Students will solve equations with the
variable on each side and equations with grouping
symbols.
S. Calahan
2008
Variables on each side
When solving equations with variables
on both sides use the Addition or
Subtraction Property of Equality to
write an equation with the variable on
only one side.
Example: 2x + 4 = x – 2
2x + 4 – x = x – 2 – x
x + 4 = -2
subtract x from each side
-2 + 10p = 8p – 1
-2 + 10p = 8p – 1
- 8p = - 8p subtract 8p from each side
-2 + 2p = -1
+2
= +2
add 2 to each side
2p = 1
divide both sides by 2
2
2 so, p = 0.5
Solve an Equation with Grouping
Symbols
To solve equations that contain
grouping symbols use the
Distributive Property to remove
the grouping symbols.
Example: 2(x + 4) = 10
2x + 8 = 10
7(m – 3) = 7
7(m – 3) = 7
7m – 21 = 7 distribute the 7
+ 21 = + 21 add 21 to each side
7m = 28
7
7
divide each side by 7
m=4
No solution
Some equations with the variable
on both sides may not have a
solution.
Example: 2x – 5 = 2x + 3
-2x
-2x
-5 = 3
2m + 5 = 5(m – 7) – 3m
2m + 5 = 5m – 35 – 3m
2m + 5 = 2m – 35 combine like terms
-2m
-2m
5 = -35
5 does not equal -35 therefore this has
no solution
An Identity
3(r + 1) – 5 = 3r – 2
3r + 3 – 5 = 3r – 2 distributive property
3r – 2 = 3r – 2
reflexive property of equality
Therefore, the solution contains
all real numbers
Steps for solving equations
1. Use the Distributive Property
2. Simplify the expression on each side.
3. Use the Addition and/or Subtraction
Properties of Equality to get the
variables on one side and the numbers
without variables on the other side.
4. Simplify the expressions on each
side of the equals sign.
4. Simplify
the
expressions
on
5. use
each side of the equals sign.
5. Use the Multiplication or
Division Property of Equality to
solve.