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`3x+8=5x-7`

We simplify the equation to the form, which is simple to understand

3x+8=5x-7

We move all terms containing x to the left and all other terms to the right.

+3x-5x=-7-8

We simplify left and right side of the equation.

-2x=-15

We divide both sides of the equation by -2 to get x.

x=7.5

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