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Solving:$ \frac{3}{7}-\frac{x-1}{2}-(2-x)=\frac{3x-4}{14} $

Could someone walk me through this, or what I'm doing wrong? I do the parenthesis, and get: $ \frac{3}{7}-\frac{x-1}{2}-2+x=\frac{3x-4}{14} $ Then I multiply everything by $14$, divide the fractions and have $6-7x-28+14x=3x-4$. Add up this and $7x-29=3x-4$. I end up with $4x=25$. Which doesn't make sense, since $x$ should equal $11/4$.

I've been going through the steps myself so long I think I'm going blind for my own mistake.

3 Answers 3

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You replace $x-1$ with $x$ in your calculation and did one of the signs wrong. The correct calculation should be

$\frac{3}{7} - \frac{x-1}{2} - (2-x) = \frac{3x - 4}{14}$

Multiplying through by $14$

$6 - 7x + 7 + -28 + 14x = 3x - 4$

Rearranging

$-7x + 14x -3x = -4 -7 - 6 + 28$

Summing up

$4x = 11$

$x = \frac{11}{4}$

as desired.

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When you multiply $\frac{3}{7}-\frac{x-1}{2}-2+x=\frac{3x-4}{14}$ by $14$ you should get $6-7x+7-28+14x=3x-4$ which becomes $4x = 11.$

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You have

$\frac{3}{7}-\frac{x-1}{2}-2+x=\frac{3x-4}{14}$

Now multiply, as you said, by 14, and you get:

$6-7(x-1)-28+14x=3x-4$

Now, watch out for the signs on the left hand side:

$6-7x+7-28+14x=3x-4$

and this adds up to

$-15+7x=3x-4$

Now adding $15$ to both sides and subtracting $3x$ you get

$4x=11$

and that's exactly what you wanted.

Your error was basically forgetting one term and doing one sign wrong.

  • 0
    That's it. The same way as you do with a $-$ in front of a fraction. Apply everything to the whole numerator.2012-05-30