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Simplifying 21y + -1[10(9 + -1y) + -7] = 6y + 2(5 + -3y) 21y + -1[(9 * 10 + -1y * 10) + -7] = 6y + 2(5 + -3y) 21y + -1[(90 + -10y) + -7] = 6y + 2(5 + -3y) Reorder the terms: 21y + -1[90 + -7 + -10y] = 6y + 2(5 + -3y) Combine like terms: 90 + -7 = 83 21y + -1[83 + -10y] = 6y + 2(5 + -3y) 21y + [83 * -1 + -10y * -1] = 6y + 2(5 + -3y) 21y + [-83 + 10y] = 6y + 2(5 + -3y) Reorder the terms: -83 + 21y + 10y = 6y + 2(5 + -3y) Combine like terms: 21y + 10y = 31y -83 + 31y = 6y + 2(5 + -3y) -83 + 31y = 6y + (5 * 2 + -3y * 2) -83 + 31y = 6y + (10 + -6y) Reorder the terms: -83 + 31y = 10 + 6y + -6y Combine like terms: 6y + -6y = 0 -83 + 31y = 10 + 0 -83 + 31y = 10 Solving -83 + 31y = 10 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '83' to each side of the equation. -83 + 83 + 31y = 10 + 83 Combine like terms: -83 + 83 = 0 0 + 31y = 10 + 83 31y = 10 + 83 Combine like terms: 10 + 83 = 93 31y = 93 Divide each side by '31'. y = 3 Simplifying y = 3
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