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Solve the equation showing ALL of your work. State if it has zero solutions, 1 solution or infinitely many solutions. Explain your reasoning. 3x - 2 = 7(x - 2) - 3(x - 3)

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3x - 2 = 7(x - 2) - 3(x - 3)

First, expand. / Your problem should look like: 3x - 2 = 7x - 14 - 3x + 9
Second, simplify 7x - 14 - 3x + 9 to 4x - 14 + 9 . / Your problem should look like: 3x - 2 = 4x - 14 + 9
Third, simplify 4x - 14 + 9 to 4x - 5./ Your problem should look like: 3x - 2 = 4x - 5
Fourth, subtract 3x from both sides. / Your problem should look like: -2 = 4x - 5 - 3x
Fifth, simplify 4x - 5 - 3x to x - 5. / Your problem should look like: -2 = x - 5
Sixth, add 5 to both sides. / Your problem should look like: -2 + 5 = x
Seventh, simplify -2 + 5 to 3. / Your problem should look like: 3 = x.
Eighth, switch sides. / Your problem should look like: x = 3

Answer: The problem only has 1 solution.

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