2(x+1)+3(x+2)=4(x+3)+5(x+4)

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Solution for 2(x+1)+3(x+2)=4(x+3)+5(x+4) equation: 


Simplifying
2(x + 1) + 3(x + 2) = 4(x + 3) + 5(x + 4)

Reorder the terms:
2(1 + x) + 3(x + 2) = 4(x + 3) + 5(x + 4)
(1 * 2 + x * 2) + 3(x + 2) = 4(x + 3) + 5(x + 4)
(2 + 2x) + 3(x + 2) = 4(x + 3) + 5(x + 4)

Reorder the terms:
2 + 2x + 3(2 + x) = 4(x + 3) + 5(x + 4)
2 + 2x + (2 * 3 + x * 3) = 4(x + 3) + 5(x + 4)
2 + 2x + (6 + 3x) = 4(x + 3) + 5(x + 4)

Reorder the terms:
2 + 6 + 2x + 3x = 4(x + 3) + 5(x + 4)

Combine like terms: 2 + 6 = 8
8 + 2x + 3x = 4(x + 3) + 5(x + 4)

Combine like terms: 2x + 3x = 5x
8 + 5x = 4(x + 3) + 5(x + 4)

Reorder the terms:
8 + 5x = 4(3 + x) + 5(x + 4)
8 + 5x = (3 * 4 + x * 4) + 5(x + 4)
8 + 5x = (12 + 4x) + 5(x + 4)

Reorder the terms:
8 + 5x = 12 + 4x + 5(4 + x)
8 + 5x = 12 + 4x + (4 * 5 + x * 5)
8 + 5x = 12 + 4x + (20 + 5x)

Reorder the terms:
8 + 5x = 12 + 20 + 4x + 5x

Combine like terms: 12 + 20 = 32
8 + 5x = 32 + 4x + 5x

Combine like terms: 4x + 5x = 9x
8 + 5x = 32 + 9x

Solving
8 + 5x = 32 + 9x

Solving for variable 'x'.

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

Add '-9x' to each side of the equation.
8 + 5x + -9x = 32 + 9x + -9x

Combine like terms: 5x + -9x = -4x
8 + -4x = 32 + 9x + -9x

Combine like terms: 9x + -9x = 0
8 + -4x = 32 + 0
8 + -4x = 32

Add '-8' to each side of the equation.
8 + -8 + -4x = 32 + -8

Combine like terms: 8 + -8 = 0
0 + -4x = 32 + -8
-4x = 32 + -8

Combine like terms: 32 + -8 = 24
-4x = 24

Divide each side by '-4'.
x = -6

Simplifying
x = -6

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