An equation is shown below
3(x-2)+7x=1/2(6x-2)
how many solutions, if any does the equation have?

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

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.