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Simplifying 5(2y + -7) + 8(y + 6) = 31 Reorder the terms: 5(-7 + 2y) + 8(y + 6) = 31 (-7 * 5 + 2y * 5) + 8(y + 6) = 31 (-35 + 10y) + 8(y + 6) = 31 Reorder the terms: -35 + 10y + 8(6 + y) = 31 -35 + 10y + (6 * 8 + y * 8) = 31 -35 + 10y + (48 + 8y) = 31 Reorder the terms: -35 + 48 + 10y + 8y = 31 Combine like terms: -35 + 48 = 13 13 + 10y + 8y = 31 Combine like terms: 10y + 8y = 18y 13 + 18y = 31 Solving 13 + 18y = 31 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + 18y = 31 + -13 Combine like terms: 13 + -13 = 0 0 + 18y = 31 + -13 18y = 31 + -13 Combine like terms: 31 + -13 = 18 18y = 18 Divide each side by '18'. y = 1 Simplifying y = 1
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