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

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


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

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

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

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

Combine like terms: -2 + 12 = 10
10 + 2x + 3x = 7(x + -2)

Combine like terms: 2x + 3x = 5x
10 + 5x = 7(x + -2)

Reorder the terms:
10 + 5x = 7(-2 + x)
10 + 5x = (-2 * 7 + x * 7)
10 + 5x = (-14 + 7x)

Solving
10 + 5x = -14 + 7x

Solving for variable 'x'.

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

Add '-7x' to each side of the equation.
10 + 5x + -7x = -14 + 7x + -7x

Combine like terms: 5x + -7x = -2x
10 + -2x = -14 + 7x + -7x

Combine like terms: 7x + -7x = 0
10 + -2x = -14 + 0
10 + -2x = -14

Add '-10' to each side of the equation.
10 + -10 + -2x = -14 + -10

Combine like terms: 10 + -10 = 0
0 + -2x = -14 + -10
-2x = -14 + -10

Combine like terms: -14 + -10 = -24
-2x = -24

Divide each side by '-2'.
x = 12

Simplifying
x = 12

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