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Simplifying 25(y + -4) + -50(2y + 3) = 75 + -125(y + 1) Reorder the terms: 25(-4 + y) + -50(2y + 3) = 75 + -125(y + 1) (-4 * 25 + y * 25) + -50(2y + 3) = 75 + -125(y + 1) (-100 + 25y) + -50(2y + 3) = 75 + -125(y + 1) Reorder the terms: -100 + 25y + -50(3 + 2y) = 75 + -125(y + 1) -100 + 25y + (3 * -50 + 2y * -50) = 75 + -125(y + 1) -100 + 25y + (-150 + -100y) = 75 + -125(y + 1) Reorder the terms: -100 + -150 + 25y + -100y = 75 + -125(y + 1) Combine like terms: -100 + -150 = -250 -250 + 25y + -100y = 75 + -125(y + 1) Combine like terms: 25y + -100y = -75y -250 + -75y = 75 + -125(y + 1) Reorder the terms: -250 + -75y = 75 + -125(1 + y) -250 + -75y = 75 + (1 * -125 + y * -125) -250 + -75y = 75 + (-125 + -125y) Combine like terms: 75 + -125 = -50 -250 + -75y = -50 + -125y Solving -250 + -75y = -50 + -125y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '125y' to each side of the equation. -250 + -75y + 125y = -50 + -125y + 125y Combine like terms: -75y + 125y = 50y -250 + 50y = -50 + -125y + 125y Combine like terms: -125y + 125y = 0 -250 + 50y = -50 + 0 -250 + 50y = -50 Add '250' to each side of the equation. -250 + 250 + 50y = -50 + 250 Combine like terms: -250 + 250 = 0 0 + 50y = -50 + 250 50y = -50 + 250 Combine like terms: -50 + 250 = 200 50y = 200 Divide each side by '50'. y = 4 Simplifying y = 4
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