1. MCC8.EE.7 a and b: Solving Equations with Variables on Both Sides.
Follow the Equation Ladder.
Simplify both sides of the equation using the distributive property and/or combining like terms.
Add/subtract to get rid of the variables on one side of the equation (think positive).
Add/subtract to get constants alone on the other side.
Multiply/divide so the variable has a coefficient of 1.

2. Equations w/ Variables on Both Sides
Linear equations can have
- exactly one solution. (We’ve seen this)
- no solution. (We haven’t seen this.)
- infinitely many solutions. (Or this.)
No solution and infinitely many solutions occur when the variable “falls out” of the equation you are trying to solve.

3. Equations w/ Variables on Both Sides
If the equation has no solution, when the variable falls out, the statement left behind is obviously false, like 4 = 7. Say, “no solution.”
If the equation has infinitely many solutions, when the variable falls out, the statement left behind is obviously true, (your book calls this an identity) like 5 = 5 or 0 = 0. Say, “infinitely many solutions” or just “many solutions.”

4. Equations w/ Variables on Both Sides
Example:
6(x + 4) = 4x + 2x – 12
< --Distribute on the left, combine like terms on the right.
6x + 24 = 6x – 12
–6x
<-- Subtract 6x on each side. 24
– 12 =
Obviously false, so equation has no solution.

5. Equations w/ Variables on Both Sides
Example:
3(x + 4) = 4 + 3x + 8
< --Distribute on the left, combine like terms on the right.
3x + 12 = 3x + 12
–3x
<-- Subtract 3x on each side. 12 =
Obviously true, so this equation has infinitely many solution.