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Simplifying 3(y + -2) + -1(5y + 2) = 3(2y + -1) + 19 Reorder the terms: 3(-2 + y) + -1(5y + 2) = 3(2y + -1) + 19 (-2 * 3 + y * 3) + -1(5y + 2) = 3(2y + -1) + 19 (-6 + 3y) + -1(5y + 2) = 3(2y + -1) + 19 Reorder the terms: -6 + 3y + -1(2 + 5y) = 3(2y + -1) + 19 -6 + 3y + (2 * -1 + 5y * -1) = 3(2y + -1) + 19 -6 + 3y + (-2 + -5y) = 3(2y + -1) + 19 Reorder the terms: -6 + -2 + 3y + -5y = 3(2y + -1) + 19 Combine like terms: -6 + -2 = -8 -8 + 3y + -5y = 3(2y + -1) + 19 Combine like terms: 3y + -5y = -2y -8 + -2y = 3(2y + -1) + 19 Reorder the terms: -8 + -2y = 3(-1 + 2y) + 19 -8 + -2y = (-1 * 3 + 2y * 3) + 19 -8 + -2y = (-3 + 6y) + 19 Reorder the terms: -8 + -2y = -3 + 19 + 6y Combine like terms: -3 + 19 = 16 -8 + -2y = 16 + 6y Solving -8 + -2y = 16 + 6y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-6y' to each side of the equation. -8 + -2y + -6y = 16 + 6y + -6y Combine like terms: -2y + -6y = -8y -8 + -8y = 16 + 6y + -6y Combine like terms: 6y + -6y = 0 -8 + -8y = 16 + 0 -8 + -8y = 16 Add '8' to each side of the equation. -8 + 8 + -8y = 16 + 8 Combine like terms: -8 + 8 = 0 0 + -8y = 16 + 8 -8y = 16 + 8 Combine like terms: 16 + 8 = 24 -8y = 24 Divide each side by '-8'. y = -3 Simplifying y = -3
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