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[tex] \frac{1}{2} x + 3 = \frac{2}{3} x + 1 \\ [/tex]
Subtract sides 3
[tex] \frac{1}{2} x + 3 - 3 = \frac{2}{3} x + 1 - 3 \\ [/tex]
[tex] \frac{1}{2} x = \frac{2}{3} x - 2 \\ [/tex]
Multiply sides by 6
[tex]6 \times \frac{1}{2} x = 6 \times \frac{2}{3} x + 6 \times ( - 2) \\ [/tex]
[tex]3x = 4x - 12[/tex]
Subtract sides 4x
[tex] - 4x + 3x = - 4x + 4x - 12[/tex]
[tex] - x = - 12[/tex]
Negatives simplifies
[tex]x = 12[/tex]
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CHECK :
[tex] \frac{1}{2} (12) + 3 = \frac{2}{3} (12) + 1 \\ [/tex]
[tex]6 + 3 = 8 + 1[/tex]
[tex]9 = 9[/tex]
Thus the solution is correct .
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