If four times a number,added to 3 is divided by the number plus 7,the result is seven halves

Assuming the number is x, we can create an equation:
(4 times x added to 3) is divided by (x plus 7), resulting in 7/2: (4*x+3)/(x+7)=7/2
Multiply both sides by x+7: 4x+3=(7/2)(x+7)
Distributive property: 4x+3=(7/2)(x)+(7/2)(7)
Move similar terms to the same side: 4x-(7/2)x=49/2-3
Combine similar terms:1/2x=43/2
Divide both sides by 1/2 (multiply both sides by 2): x=43
The number is 43.

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