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

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


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

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

Reorder the terms:
-7 + 7x + -4(3 + 2x) = 2(x + 1) + -3(4 + -1x)
-7 + 7x + (3 * -4 + 2x * -4) = 2(x + 1) + -3(4 + -1x)
-7 + 7x + (-12 + -8x) = 2(x + 1) + -3(4 + -1x)

Reorder the terms:
-7 + -12 + 7x + -8x = 2(x + 1) + -3(4 + -1x)

Combine like terms: -7 + -12 = -19
-19 + 7x + -8x = 2(x + 1) + -3(4 + -1x)

Combine like terms: 7x + -8x = -1x
-19 + -1x = 2(x + 1) + -3(4 + -1x)

Reorder the terms:
-19 + -1x = 2(1 + x) + -3(4 + -1x)
-19 + -1x = (1 * 2 + x * 2) + -3(4 + -1x)
-19 + -1x = (2 + 2x) + -3(4 + -1x)
-19 + -1x = 2 + 2x + (4 * -3 + -1x * -3)
-19 + -1x = 2 + 2x + (-12 + 3x)

Reorder the terms:
-19 + -1x = 2 + -12 + 2x + 3x

Combine like terms: 2 + -12 = -10
-19 + -1x = -10 + 2x + 3x

Combine like terms: 2x + 3x = 5x
-19 + -1x = -10 + 5x

Solving
-19 + -1x = -10 + 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.
-19 + -1x + -5x = -10 + 5x + -5x

Combine like terms: -1x + -5x = -6x
-19 + -6x = -10 + 5x + -5x

Combine like terms: 5x + -5x = 0
-19 + -6x = -10 + 0
-19 + -6x = -10

Add '19' to each side of the equation.
-19 + 19 + -6x = -10 + 19

Combine like terms: -19 + 19 = 0
0 + -6x = -10 + 19
-6x = -10 + 19

Combine like terms: -10 + 19 = 9
-6x = 9

Divide each side by '-6'.
x = -1.5

Simplifying
x = -1.5

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