Question

What is the solution to the equation 1/2 x + 3 = 2/3 x + 1​

Answer 1

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`(1)/(2) x + 3 = (2)/(3) x + 1 \\`

Subtract sides 3

`(1)/(2) x + 3 - 3 = (2)/(3) x + 1 - 3 \\`

`(1)/(2) x = (2)/(3) x - 2 \\`

Multiply sides by 6

`6 * (1)/(2) x = 6 * (2)/(3) x + 6 * ( - 2) \\`

`3x = 4x - 12`

Subtract sides 4x

`- 4x + 3x = - 4x + 4x - 12`

`- x = - 12`

Negatives simplifies

`x = 12`

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CHECK :

`(1)/(2) (12) + 3 = (2)/(3) (12) + 1 \\`

`6 + 3 = 8 + 1`

`9 = 9`

Thus the solution is correct .

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