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

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

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

Reorder the terms:
7(4 + x) + -2(x + -3) = 2(z + -2) + 2(x + -1)
(4 * 7 + x * 7) + -2(x + -3) = 2(z + -2) + 2(x + -1)
(28 + 7x) + -2(x + -3) = 2(z + -2) + 2(x + -1)

Reorder the terms:
28 + 7x + -2(-3 + x) = 2(z + -2) + 2(x + -1)
28 + 7x + (-3 * -2 + x * -2) = 2(z + -2) + 2(x + -1)
28 + 7x + (6 + -2x) = 2(z + -2) + 2(x + -1)

Reorder the terms:
28 + 6 + 7x + -2x = 2(z + -2) + 2(x + -1)

Combine like terms: 28 + 6 = 34
34 + 7x + -2x = 2(z + -2) + 2(x + -1)

Combine like terms: 7x + -2x = 5x
34 + 5x = 2(z + -2) + 2(x + -1)

Reorder the terms:
34 + 5x = 2(-2 + z) + 2(x + -1)
34 + 5x = (-2 * 2 + z * 2) + 2(x + -1)
34 + 5x = (-4 + 2z) + 2(x + -1)

Reorder the terms:
34 + 5x = -4 + 2z + 2(-1 + x)
34 + 5x = -4 + 2z + (-1 * 2 + x * 2)
34 + 5x = -4 + 2z + (-2 + 2x)

Reorder the terms:
34 + 5x = -4 + -2 + 2x + 2z

Combine like terms: -4 + -2 = -6
34 + 5x = -6 + 2x + 2z

Solving
34 + 5x = -6 + 2x + 2z

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.
34 + 5x + -2x = -6 + 2x + -2x + 2z

Combine like terms: 5x + -2x = 3x
34 + 3x = -6 + 2x + -2x + 2z

Combine like terms: 2x + -2x = 0
34 + 3x = -6 + 0 + 2z
34 + 3x = -6 + 2z

Add '-34' to each side of the equation.
34 + -34 + 3x = -6 + -34 + 2z

Combine like terms: 34 + -34 = 0
0 + 3x = -6 + -34 + 2z
3x = -6 + -34 + 2z

Combine like terms: -6 + -34 = -40
3x = -40 + 2z

Divide each side by '3'.
x = -13.33333333 + 0.6666666667z

Simplifying
x = -13.33333333 + 0.6666666667z