Answer:
Step-by-step explanation:
It is often recommended that you "clear fractions" first when solving an equation involving fractions. Here, you can do that by multiplying both sides of the equation by 6.
5x -2 = 12x -30
Now, you can add 30-5x to both sides to put x-terms on one side and constant terms on the other:
28 = 7x
Finally, divide by 7 to get the value of x.
4 = x
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Just to show you that there are other ways, we can subtract the left side of the equation from both sides:
0 = (2 -5/6)x -(5 -1/3)
0 = 7/6x - 14/3 . . . . simplify
Multiplying by 6/7 will make the coefficient of x be 1:
0 = x - (14/3)(6/7) = x - 4
4 = x . . . . . . add 4
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Comment on the solution method(s)
We note that there are x-terms on both sides of the equation. The one on the left has a coefficient of 5/6; the one on the right a coefficient of 2. In order to combine these terms we need to add the opposite of one of them to both sides of the equation.
If we choose to add the opposite of the term with the smallest (least positive) coefficient, then the resulting x-term will have a positive coefficient. This can make life easier because later you will be dividing by a positive number, not a negative one.
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At the end of the second solution, we multiplied by 6/7. These numbers may look familiar, because in our first solution we started off by multiplying by 6 and ended up by dividing by 7. The advantage of the first solution method is that we didn't have to do any arithmetic with fractions after the first multiplication. If you're comfortable with fractions, then it isn't really necessary to "clear fractions" first, as the second solution shows.
