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I am a a student and I am having difficulty with answering this question. I keep getting the answer wrong. Please may I have a step by step solution to this question so that I won't have difficulties with answering these type of questions in the future.

Solve

$\displaystyle\frac{3x}{4} + \displaystyle\frac{2}{3} = x$

$x$= ____

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    What answer _do_ you get, and how do you get there? – 2017-01-27
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    Hint : First of all, multiply with $12$ to get rid of the denominators. – 2017-01-27
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    I got x = -2/3. By subtracting -2/3 and then times by 4. Then I don't know what to do next. – 2017-01-27
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    How do u multiply with 12 – 2017-01-27
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    You multiply the equation with $12$. You get $9x+8=12x$. The rest should be easy. – 2017-01-27
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    Thank you very much to everyone that commented and answered – 2017-01-27
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    "How do u multiply with 12". That's difficult to explain, but it suffices to know how to multiply by $2$ and $3$. – 2017-01-27
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    In general, you have to find a common denominator. It is best, if you find the least common multiplier, but this is not necessary. It is sufficient to take the product of all occuring denominators. If you multiply the equation with this product, all denominators will vanish. If there is an $x$ in one or more denominators, you have to be careful because values for which one denominator is zero are not allowed. But apparantly, at the moment you do not have such exercises :) – 2017-01-27
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    @OliviaAages If you still have any questions, ask them. – 2017-01-27
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    @OliviaAages Remark : It is not necessary to get rid of the denominators, but it makes the calculation much easier. – 2017-01-27
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    I understand what you have to do now – 2017-01-27

5 Answers 5

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$$\frac{3x}{4} + \frac23 = x \implies \frac{9x+8}{12} = x \implies 9x+8 = 12 x \implies 8 = 3 x \implies x = \frac83.$$

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multiplying by $12$ we obtain $$9x+8=12x$$ from here (by sbtracting $9x$) we obtain $$3x=8$$ or $$x=\frac{8}{3}$$

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One basic concept for you. Hope its help.

Always take variable terms on left side and constant terms on right side. Then solve.

$\frac{3x}{4} - x = \frac{-2}{3}$

$\frac{3x - 4x}{4} = \frac{-2}{3}$

$\frac{-x}{4} = \frac{-2}{3}$

$x = \frac{-2}{3} × - 4$

$x = \frac 83$

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$$\frac{3x}{4}+\frac{2}{3}=x$$ Notice $\frac{3x}{4}=\frac{3}{4}x$

Now, rewrite the equation as: $$\frac{3}{4}x+\frac{2}{3}=x$$ Now, we need to get our "like terms together. To get our like terms together, we subtract $\frac{3}{4}x$ on both sides. To subtract these, we must find a common denominator. x has a coefficient of 1 in front of it. So, we are subtracting $1x-\frac{3}{4}x$. Or, equivalently (finding a common denominator), we may subtract $$\frac{4}{4}x-\frac{3}{4}x$$. This equals $$\frac{1}{4}x$$ So, now our equation is $$\frac{2}{3}=\frac{1}{4}x$$. We are still trying to isolate x. When x is multiplied by a fraction we may multiply by the reciprocal of the coefficient. The reciprocal of $\frac{1}{4}$ is $\frac{4}{1}$. Now, we multiply both sides of the equation by $\frac{4}{1}$. This leaves $$\frac{8}{3}=x$$

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Just see here... enter image description here

Hope it helps !!!

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    Isn't it the same as https://math.stackexchange.com/questions/2116717/algebraic-fractions-grade-10/2116719#2116719 – 2017-02-01
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    @ Harsh Kumar, yeah – 2017-02-02