# MCC8.EE.7 a and b: Solving Equations with Variables on Both Sides.

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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.

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.

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.”

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.

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.

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