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Question
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[tex] \frac{2}{3}x - \frac{1}{2} = x + \frac{7}{6} [/tex]
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Rewrite the right to the left
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[tex] x + \frac{7}{6} = \frac{2}{3}x - \frac{1}{2}[/tex]
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Take away 2/3x from both sides
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[tex] x + \frac{7}{6} - \frac{2}{3}x= \frac{2}{3}x - \frac{1}{2} - \frac{2}{3}x[/tex]
[tex] x - \frac{2}{3}x + \frac{7}{6}= \frac{2}{3}x - \frac{2}{3}x - \frac{1}{2}[/tex]
[tex] \frac{7}{6} + \frac{1}{3}x= - \frac{1}{2} [/tex]
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Take away 7/6 from both sides
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[tex] \frac{7}{6} + \frac{1}{3}x - \frac{7}{6} = - \frac{1}{2} - \frac{7}{6}
[/tex]
[tex] \frac{7}{6} - \frac{7}{6} + \frac{1}{3}x = - \frac{1}{2} - \frac{7}{6} [/tex]
[tex] \frac{1}{3}x = - \frac{1}{2} - \frac{7}{6}[/tex]
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Change the denominator to be the same and minus
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[tex] \frac{1}{3}x = - \frac{3}{6} - \frac{7}{6} [/tex]
[tex] \frac{1}{3}x = - \frac{10}{6} [/tex]
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Multiply by 6 on both sides
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[tex]2x= -10[/tex]
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Divide by 2 both sides
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[tex]x = -5[/tex]
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Answer : x = -5
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