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

 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

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 4 4 x = – 3

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 +2p 10p = 40 10 10 p = 4

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 – 4 3x = –15 3 3 x = –5

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

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