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Simplifying (y + 12) = 0.5[(2y + 8) + (y + -2)] Reorder the terms: (12 + y) = 0.5[(2y + 8) + (y + -2)] Remove parenthesis around (12 + y) 12 + y = 0.5[(2y + 8) + (y + -2)] Reorder the terms: 12 + y = 0.5[(8 + 2y) + (y + -2)] Remove parenthesis around (8 + 2y) 12 + y = 0.5[8 + 2y + (y + -2)] Reorder the terms: 12 + y = 0.5[8 + 2y + (-2 + y)] Remove parenthesis around (-2 + y) 12 + y = 0.5[8 + 2y + -2 + y] Reorder the terms: 12 + y = 0.5[8 + -2 + 2y + y] Combine like terms: 8 + -2 = 6 12 + y = 0.5[6 + 2y + y] Combine like terms: 2y + y = 3y 12 + y = 0.5[6 + 3y] 12 + y = [6 * 0.5 + 3y * 0.5] 12 + y = [3 + 1.5y] Solving 12 + y = 3 + 1.5y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5y' to each side of the equation. 12 + y + -1.5y = 3 + 1.5y + -1.5y Combine like terms: y + -1.5y = -0.5y 12 + -0.5y = 3 + 1.5y + -1.5y Combine like terms: 1.5y + -1.5y = 0.0 12 + -0.5y = 3 + 0.0 12 + -0.5y = 3 Add '-12' to each side of the equation. 12 + -12 + -0.5y = 3 + -12 Combine like terms: 12 + -12 = 0 0 + -0.5y = 3 + -12 -0.5y = 3 + -12 Combine like terms: 3 + -12 = -9 -0.5y = -9 Divide each side by '-0.5'. y = 18 Simplifying y = 18
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