Q:

# 2/3x-1/2=x+7/6 How do I do this?Please give step by step

Accepted Solution

A:
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Question
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$$\frac{2}{3}x - \frac{1}{2} = x + \frac{7}{6}$$

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Rewrite the right to the left
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$$x + \frac{7}{6} = \frac{2}{3}x - \frac{1}{2}$$

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Take away 2/3x from both sides
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$$x + \frac{7}{6} - \frac{2}{3}x= \frac{2}{3}x - \frac{1}{2} - \frac{2}{3}x$$
$$x - \frac{2}{3}x + \frac{7}{6}= \frac{2}{3}x - \frac{2}{3}x - \frac{1}{2}$$
$$\frac{7}{6} + \frac{1}{3}x= - \frac{1}{2}$$

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Take away 7/6 from both sides
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$$\frac{7}{6} + \frac{1}{3}x - \frac{7}{6} = - \frac{1}{2} - \frac{7}{6}$$
$$\frac{7}{6} - \frac{7}{6} + \frac{1}{3}x = - \frac{1}{2} - \frac{7}{6}$$
$$\frac{1}{3}x = - \frac{1}{2} - \frac{7}{6}$$

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Change the denominator to be the same and minus
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$$\frac{1}{3}x = - \frac{3}{6} - \frac{7}{6}$$
$$\frac{1}{3}x = - \frac{10}{6}$$

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Multiply by 6 on both sides
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$$2x= -10$$

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Divide by 2  both sides
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$$x = -5$$

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