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Simplifying -5(2y + 1) + -3(1 + -1y) = 2(4y + 1) + -3 Reorder the terms: -5(1 + 2y) + -3(1 + -1y) = 2(4y + 1) + -3 (1 * -5 + 2y * -5) + -3(1 + -1y) = 2(4y + 1) + -3 (-5 + -10y) + -3(1 + -1y) = 2(4y + 1) + -3 -5 + -10y + (1 * -3 + -1y * -3) = 2(4y + 1) + -3 -5 + -10y + (-3 + 3y) = 2(4y + 1) + -3 Reorder the terms: -5 + -3 + -10y + 3y = 2(4y + 1) + -3 Combine like terms: -5 + -3 = -8 -8 + -10y + 3y = 2(4y + 1) + -3 Combine like terms: -10y + 3y = -7y -8 + -7y = 2(4y + 1) + -3 Reorder the terms: -8 + -7y = 2(1 + 4y) + -3 -8 + -7y = (1 * 2 + 4y * 2) + -3 -8 + -7y = (2 + 8y) + -3 Reorder the terms: -8 + -7y = 2 + -3 + 8y Combine like terms: 2 + -3 = -1 -8 + -7y = -1 + 8y Solving -8 + -7y = -1 + 8y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-8y' to each side of the equation. -8 + -7y + -8y = -1 + 8y + -8y Combine like terms: -7y + -8y = -15y -8 + -15y = -1 + 8y + -8y Combine like terms: 8y + -8y = 0 -8 + -15y = -1 + 0 -8 + -15y = -1 Add '8' to each side of the equation. -8 + 8 + -15y = -1 + 8 Combine like terms: -8 + 8 = 0 0 + -15y = -1 + 8 -15y = -1 + 8 Combine like terms: -1 + 8 = 7 -15y = 7 Divide each side by '-15'. y = -0.4666666667 Simplifying y = -0.4666666667
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