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Simplifying 3y + 2 + -4(y + 1) = 3(y + 2) + -2(5y + 1) Reorder the terms: 3y + 2 + -4(1 + y) = 3(y + 2) + -2(5y + 1) 3y + 2 + (1 * -4 + y * -4) = 3(y + 2) + -2(5y + 1) 3y + 2 + (-4 + -4y) = 3(y + 2) + -2(5y + 1) Reorder the terms: 2 + -4 + 3y + -4y = 3(y + 2) + -2(5y + 1) Combine like terms: 2 + -4 = -2 -2 + 3y + -4y = 3(y + 2) + -2(5y + 1) Combine like terms: 3y + -4y = -1y -2 + -1y = 3(y + 2) + -2(5y + 1) Reorder the terms: -2 + -1y = 3(2 + y) + -2(5y + 1) -2 + -1y = (2 * 3 + y * 3) + -2(5y + 1) -2 + -1y = (6 + 3y) + -2(5y + 1) Reorder the terms: -2 + -1y = 6 + 3y + -2(1 + 5y) -2 + -1y = 6 + 3y + (1 * -2 + 5y * -2) -2 + -1y = 6 + 3y + (-2 + -10y) Reorder the terms: -2 + -1y = 6 + -2 + 3y + -10y Combine like terms: 6 + -2 = 4 -2 + -1y = 4 + 3y + -10y Combine like terms: 3y + -10y = -7y -2 + -1y = 4 + -7y Solving -2 + -1y = 4 + -7y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7y' to each side of the equation. -2 + -1y + 7y = 4 + -7y + 7y Combine like terms: -1y + 7y = 6y -2 + 6y = 4 + -7y + 7y Combine like terms: -7y + 7y = 0 -2 + 6y = 4 + 0 -2 + 6y = 4 Add '2' to each side of the equation. -2 + 2 + 6y = 4 + 2 Combine like terms: -2 + 2 = 0 0 + 6y = 4 + 2 6y = 4 + 2 Combine like terms: 4 + 2 = 6 6y = 6 Divide each side by '6'. y = 1 Simplifying y = 1
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