0.5(x-2)-2(x-5)=0.9(x-5)-5(x-2)

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Solution for 0.5(x-2)-2(x-5)=0.9(x-5)-5(x-2) equation: 


Simplifying
0.5(x + -2) + -2(x + -5) = 0.9(x + -5) + -5(x + -2)

Reorder the terms:
0.5(-2 + x) + -2(x + -5) = 0.9(x + -5) + -5(x + -2)
(-2 * 0.5 + x * 0.5) + -2(x + -5) = 0.9(x + -5) + -5(x + -2)
(-1 + 0.5x) + -2(x + -5) = 0.9(x + -5) + -5(x + -2)

Reorder the terms:
-1 + 0.5x + -2(-5 + x) = 0.9(x + -5) + -5(x + -2)
-1 + 0.5x + (-5 * -2 + x * -2) = 0.9(x + -5) + -5(x + -2)
-1 + 0.5x + (10 + -2x) = 0.9(x + -5) + -5(x + -2)

Reorder the terms:
-1 + 10 + 0.5x + -2x = 0.9(x + -5) + -5(x + -2)

Combine like terms: -1 + 10 = 9
9 + 0.5x + -2x = 0.9(x + -5) + -5(x + -2)

Combine like terms: 0.5x + -2x = -1.5x
9 + -1.5x = 0.9(x + -5) + -5(x + -2)

Reorder the terms:
9 + -1.5x = 0.9(-5 + x) + -5(x + -2)
9 + -1.5x = (-5 * 0.9 + x * 0.9) + -5(x + -2)
9 + -1.5x = (-4.5 + 0.9x) + -5(x + -2)

Reorder the terms:
9 + -1.5x = -4.5 + 0.9x + -5(-2 + x)
9 + -1.5x = -4.5 + 0.9x + (-2 * -5 + x * -5)
9 + -1.5x = -4.5 + 0.9x + (10 + -5x)

Reorder the terms:
9 + -1.5x = -4.5 + 10 + 0.9x + -5x

Combine like terms: -4.5 + 10 = 5.5
9 + -1.5x = 5.5 + 0.9x + -5x

Combine like terms: 0.9x + -5x = -4.1x
9 + -1.5x = 5.5 + -4.1x

Solving
9 + -1.5x = 5.5 + -4.1x

Solving for variable 'x'.

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

Add '4.1x' to each side of the equation.
9 + -1.5x + 4.1x = 5.5 + -4.1x + 4.1x

Combine like terms: -1.5x + 4.1x = 2.6x
9 + 2.6x = 5.5 + -4.1x + 4.1x

Combine like terms: -4.1x + 4.1x = 0.0
9 + 2.6x = 5.5 + 0.0
9 + 2.6x = 5.5

Add '-9' to each side of the equation.
9 + -9 + 2.6x = 5.5 + -9

Combine like terms: 9 + -9 = 0
0 + 2.6x = 5.5 + -9
2.6x = 5.5 + -9

Combine like terms: 5.5 + -9 = -3.5
2.6x = -3.5

Divide each side by '2.6'.
x = -1.346153846

Simplifying
x = -1.346153846

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