Step-by-step explanation:
In order to find the number of solutions, we have to expand both sides out first.
[tex]3(x - 2) + 7x = \frac{1}{2} (6x - 2)[/tex]
First, expand 3(x-2), which will obtain 3x-6.
Next, expand (1/2)(6x-2), which gives 3x - 1.
The result at this point should be as shown below:
[tex]3x - 6 + 7x = 3x - 1[/tex]
Now, we would shift all x terms to the left and all number terms to the right.
[tex]3x + 7x - 3x = - 1 + 6[/tex]
After simplifying, the final equation would be:
[tex]7x = 5[/tex]
This is a linear equation and it has one solution.
[tex]x = \frac{5}{7} [/tex]
