5(x+2)-(x-3)=2(x-5)

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


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

Reorder the terms:
5(2 + x) + -1(x + -3) = 2(x + -5)
(2 * 5 + x * 5) + -1(x + -3) = 2(x + -5)
(10 + 5x) + -1(x + -3) = 2(x + -5)

Reorder the terms:
10 + 5x + -1(-3 + x) = 2(x + -5)
10 + 5x + (-3 * -1 + x * -1) = 2(x + -5)
10 + 5x + (3 + -1x) = 2(x + -5)

Reorder the terms:
10 + 3 + 5x + -1x = 2(x + -5)

Combine like terms: 10 + 3 = 13
13 + 5x + -1x = 2(x + -5)

Combine like terms: 5x + -1x = 4x
13 + 4x = 2(x + -5)

Reorder the terms:
13 + 4x = 2(-5 + x)
13 + 4x = (-5 * 2 + x * 2)
13 + 4x = (-10 + 2x)

Solving
13 + 4x = -10 + 2x

Solving for variable 'x'.

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

Add '-2x' to each side of the equation.
13 + 4x + -2x = -10 + 2x + -2x

Combine like terms: 4x + -2x = 2x
13 + 2x = -10 + 2x + -2x

Combine like terms: 2x + -2x = 0
13 + 2x = -10 + 0
13 + 2x = -10

Add '-13' to each side of the equation.
13 + -13 + 2x = -10 + -13

Combine like terms: 13 + -13 = 0
0 + 2x = -10 + -13
2x = -10 + -13

Combine like terms: -10 + -13 = -23
2x = -23

Divide each side by '2'.
x = -11.5

Simplifying
x = -11.5

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