Download 3.4 Solving Equations with Variables on Both Sides

3.4
Solving Equations
with Variables on Both Sides
Objective: Solve equations that have variables
on both sides.
What do we do when variables appear on
both sides of the equation?
Equations with Variables on
Both Sides
• Some equations have variables on both sides
• To solve these equations, you can first collect the
variable terms on one side of the equation
• Collecting the variable terms on the side with the
greater variable coefficient will result in a positive
coefficient
Solve
7x + 19 = -2x + 55
30 – 9y = 6y
Solve
34 – 3x = 14x
5y – 2 = y + 10
Solve
-6x + 4 = -8x
3x – 10 + 4x = 5x – 7
Solve
5x – 3x + 4 = 3x + 8
6x + 3 = 8 + 7x + 2x
Number of Solutions
• So far you have seen linear equations that have only one
solution.
• Some linear equations have no solution.
• No solution occurs when you end up with a false statement
• 6≠4
• An identity is an equation that is true for all values of the
variable. An identity has infinitely many solutions.
• Infinitely many solutions occur when you a get a number
equal to itself
• 6=6
Solve the equation and determine
how many solutions it has.
3(x + 2) = 3x + 6
3(x + 2) = 3x + 4
3(x + 2) = 2x + 4
Solve the equation if possible and
determine the number of solutions.
2(x + 4) = 2x + 8
2( x + 4) = x - 8
Solve the equation if possible and
determine the number of solutions.
2(x + 4) = 2x – 8
2(x + 4) = x + 8