3(x-2)+4(x-1)=7(x+2)-2(x-3)

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Solution for 3(x-2)+4(x-1)=7(x+2)-2(x-3) equation: 


Simplifying
3(x + -2) + 4(x + -1) = 7(x + 2) + -2(x + -3)

Reorder the terms:
3(-2 + x) + 4(x + -1) = 7(x + 2) + -2(x + -3)
(-2 * 3 + x * 3) + 4(x + -1) = 7(x + 2) + -2(x + -3)
(-6 + 3x) + 4(x + -1) = 7(x + 2) + -2(x + -3)

Reorder the terms:
-6 + 3x + 4(-1 + x) = 7(x + 2) + -2(x + -3)
-6 + 3x + (-1 * 4 + x * 4) = 7(x + 2) + -2(x + -3)
-6 + 3x + (-4 + 4x) = 7(x + 2) + -2(x + -3)

Reorder the terms:
-6 + -4 + 3x + 4x = 7(x + 2) + -2(x + -3)

Combine like terms: -6 + -4 = -10
-10 + 3x + 4x = 7(x + 2) + -2(x + -3)

Combine like terms: 3x + 4x = 7x
-10 + 7x = 7(x + 2) + -2(x + -3)

Reorder the terms:
-10 + 7x = 7(2 + x) + -2(x + -3)
-10 + 7x = (2 * 7 + x * 7) + -2(x + -3)
-10 + 7x = (14 + 7x) + -2(x + -3)

Reorder the terms:
-10 + 7x = 14 + 7x + -2(-3 + x)
-10 + 7x = 14 + 7x + (-3 * -2 + x * -2)
-10 + 7x = 14 + 7x + (6 + -2x)

Reorder the terms:
-10 + 7x = 14 + 6 + 7x + -2x

Combine like terms: 14 + 6 = 20
-10 + 7x = 20 + 7x + -2x

Combine like terms: 7x + -2x = 5x
-10 + 7x = 20 + 5x

Solving
-10 + 7x = 20 + 5x

Solving for variable 'x'.

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

Add '-5x' to each side of the equation.
-10 + 7x + -5x = 20 + 5x + -5x

Combine like terms: 7x + -5x = 2x
-10 + 2x = 20 + 5x + -5x

Combine like terms: 5x + -5x = 0
-10 + 2x = 20 + 0
-10 + 2x = 20

Add '10' to each side of the equation.
-10 + 10 + 2x = 20 + 10

Combine like terms: -10 + 10 = 0
0 + 2x = 20 + 10
2x = 20 + 10

Combine like terms: 20 + 10 = 30
2x = 30

Divide each side by '2'.
x = 15

Simplifying
x = 15

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