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Simplifying 6(y + 3) + 2(y + 7) = 7(y + 3) Reorder the terms: 6(3 + y) + 2(y + 7) = 7(y + 3) (3 * 6 + y * 6) + 2(y + 7) = 7(y + 3) (18 + 6y) + 2(y + 7) = 7(y + 3) Reorder the terms: 18 + 6y + 2(7 + y) = 7(y + 3) 18 + 6y + (7 * 2 + y * 2) = 7(y + 3) 18 + 6y + (14 + 2y) = 7(y + 3) Reorder the terms: 18 + 14 + 6y + 2y = 7(y + 3) Combine like terms: 18 + 14 = 32 32 + 6y + 2y = 7(y + 3) Combine like terms: 6y + 2y = 8y 32 + 8y = 7(y + 3) Reorder the terms: 32 + 8y = 7(3 + y) 32 + 8y = (3 * 7 + y * 7) 32 + 8y = (21 + 7y) Solving 32 + 8y = 21 + 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. 32 + 8y + -7y = 21 + 7y + -7y Combine like terms: 8y + -7y = 1y 32 + 1y = 21 + 7y + -7y Combine like terms: 7y + -7y = 0 32 + 1y = 21 + 0 32 + 1y = 21 Add '-32' to each side of the equation. 32 + -32 + 1y = 21 + -32 Combine like terms: 32 + -32 = 0 0 + 1y = 21 + -32 1y = 21 + -32 Combine like terms: 21 + -32 = -11 1y = -11 Divide each side by '1'. y = -11 Simplifying y = -11
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