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Simplifying 4z + 5 + 10y + 7 = 5z + -6 + 12y + -7 Reorder the terms: 5 + 7 + 10y + 4z = 5z + -6 + 12y + -7 Combine like terms: 5 + 7 = 12 12 + 10y + 4z = 5z + -6 + 12y + -7 Reorder the terms: 12 + 10y + 4z = -6 + -7 + 12y + 5z Combine like terms: -6 + -7 = -13 12 + 10y + 4z = -13 + 12y + 5z Solving 12 + 10y + 4z = -13 + 12y + 5z Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-12y' to each side of the equation. 12 + 10y + -12y + 4z = -13 + 12y + -12y + 5z Combine like terms: 10y + -12y = -2y 12 + -2y + 4z = -13 + 12y + -12y + 5z Combine like terms: 12y + -12y = 0 12 + -2y + 4z = -13 + 0 + 5z 12 + -2y + 4z = -13 + 5z Add '-12' to each side of the equation. 12 + -2y + -12 + 4z = -13 + -12 + 5z Reorder the terms: 12 + -12 + -2y + 4z = -13 + -12 + 5z Combine like terms: 12 + -12 = 0 0 + -2y + 4z = -13 + -12 + 5z -2y + 4z = -13 + -12 + 5z Combine like terms: -13 + -12 = -25 -2y + 4z = -25 + 5z Add '-4z' to each side of the equation. -2y + 4z + -4z = -25 + 5z + -4z Combine like terms: 4z + -4z = 0 -2y + 0 = -25 + 5z + -4z -2y = -25 + 5z + -4z Combine like terms: 5z + -4z = 1z -2y = -25 + 1z Divide each side by '-2'. y = 12.5 + -0.5z Simplifying y = 12.5 + -0.5z
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