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Simplifying 7(3y + 5) + -4(2y + -3) = 5(y + -1) Reorder the terms: 7(5 + 3y) + -4(2y + -3) = 5(y + -1) (5 * 7 + 3y * 7) + -4(2y + -3) = 5(y + -1) (35 + 21y) + -4(2y + -3) = 5(y + -1) Reorder the terms: 35 + 21y + -4(-3 + 2y) = 5(y + -1) 35 + 21y + (-3 * -4 + 2y * -4) = 5(y + -1) 35 + 21y + (12 + -8y) = 5(y + -1) Reorder the terms: 35 + 12 + 21y + -8y = 5(y + -1) Combine like terms: 35 + 12 = 47 47 + 21y + -8y = 5(y + -1) Combine like terms: 21y + -8y = 13y 47 + 13y = 5(y + -1) Reorder the terms: 47 + 13y = 5(-1 + y) 47 + 13y = (-1 * 5 + y * 5) 47 + 13y = (-5 + 5y) Solving 47 + 13y = -5 + 5y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5y' to each side of the equation. 47 + 13y + -5y = -5 + 5y + -5y Combine like terms: 13y + -5y = 8y 47 + 8y = -5 + 5y + -5y Combine like terms: 5y + -5y = 0 47 + 8y = -5 + 0 47 + 8y = -5 Add '-47' to each side of the equation. 47 + -47 + 8y = -5 + -47 Combine like terms: 47 + -47 = 0 0 + 8y = -5 + -47 8y = -5 + -47 Combine like terms: -5 + -47 = -52 8y = -52 Divide each side by '8'. y = -6.5 Simplifying y = -6.5
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