32(10-3.5x)=13(3x-8)+46.5

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Solution for 32(10-3.5x)=13(3x-8)+46.5 equation: 


Simplifying
32(10 + -3.5x) = 13(3x + -8) + 46.5
(10 * 32 + -3.5x * 32) = 13(3x + -8) + 46.5
(320 + -112x) = 13(3x + -8) + 46.5

Reorder the terms:
320 + -112x = 13(-8 + 3x) + 46.5
320 + -112x = (-8 * 13 + 3x * 13) + 46.5
320 + -112x = (-104 + 39x) + 46.5

Reorder the terms:
320 + -112x = -104 + 46.5 + 39x

Combine like terms: -104 + 46.5 = -57.5
320 + -112x = -57.5 + 39x

Solving
320 + -112x = -57.5 + 39x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-39x' to each side of the equation.
320 + -112x + -39x = -57.5 + 39x + -39x

Combine like terms: -112x + -39x = -151x
320 + -151x = -57.5 + 39x + -39x

Combine like terms: 39x + -39x = 0
320 + -151x = -57.5 + 0
320 + -151x = -57.5

Add '-320' to each side of the equation.
320 + -320 + -151x = -57.5 + -320

Combine like terms: 320 + -320 = 0
0 + -151x = -57.5 + -320
-151x = -57.5 + -320

Combine like terms: -57.5 + -320 = -377.5
-151x = -377.5

Divide each side by '-151'.
x = 2.5

Simplifying
x = 2.5

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