Answer:
one solution: x = 5/7
Step-by-step explanation:
Eliminating parentheses, you have ...
3x -6 +7x = 3x -1
10x -6 = 3x -1 . . . . . collect terms
7x -6 = -1 . . . . . . . . . subtract 3x
7x = 5 . . . . . . . . . . . add 6
x = 5/7 . . . . . . . . . . divide by 7
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One way to answer a question like this is to subtract one side from the equation, so it is <something> = 0.
If the <something> is 0, there are infinite solutions.
If the <something> is a constant not zero, there are no solutions.
If the <something> is a linear expression with a variable in it, there will be one solution.
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Doing that here gives ...
3(x -2) +7x -1/2(6x -2) = 0 . . subtract the right side
3x -6 +7x -3x +1 = 0 . . . . . . eliminate parens
7x -5 = 0 . . . . . . . . . . . . . . . . collect terms. There is one solution.
