1. Solving Equations with Variables on Both Sides
Section 2.5
Solving Equations with Variables on Both Sides

2.  switch sides  switch signs
Method:
Apply the Dist. Prop.: a(b + c) = ab + ac
Comb. like terms on same side of = sign.
Add or subtract a variable expression to get the terms on the same side of the equation.
Add or subtract to get variable alone.
Multiply or divide to get coefficient to be 1.
 switch sides  switch signs

3. 5x = 1x – 12 –1x –1x 4x = –12 4 4 x = – 3 Solve each equation.1.
5x = 1x – 12
Isolate the 12 by eliminating x.
–1x –1x
4x = –12
x = – 3

4. 2. 5p + 3p = 40 – 2p 10p = 40 10 10 p = 4 +2p +2p 8p = 40 – 2p Combine
like terms.
8p = 40 – 2p
Isolate the 40 by eliminating –2p.
+2p p
10p = 40
p = 4

5. 3. 6x + 2(x + 2) = 5x – 11
Distribute.
6x + 2x + 4 = 5x – 11
Combine
Like Terms.
8x + 4 = 5x – 11
–5x –5x
3x + 4 = –11
– – 4
3x = –15
x = –5

6. What is the next line that should be written to solve the equation: 5x + 1 = 17 – 3x ?

7. What is the next line that should be written to solve the equation: 5x – 7 + 3x = 70 + x ?