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Simplifying 6(y + -4) + 4(5y + 1) = 3(y + -2) + -4(2y + 1) Reorder the terms: 6(-4 + y) + 4(5y + 1) = 3(y + -2) + -4(2y + 1) (-4 * 6 + y * 6) + 4(5y + 1) = 3(y + -2) + -4(2y + 1) (-24 + 6y) + 4(5y + 1) = 3(y + -2) + -4(2y + 1) Reorder the terms: -24 + 6y + 4(1 + 5y) = 3(y + -2) + -4(2y + 1) -24 + 6y + (1 * 4 + 5y * 4) = 3(y + -2) + -4(2y + 1) -24 + 6y + (4 + 20y) = 3(y + -2) + -4(2y + 1) Reorder the terms: -24 + 4 + 6y + 20y = 3(y + -2) + -4(2y + 1) Combine like terms: -24 + 4 = -20 -20 + 6y + 20y = 3(y + -2) + -4(2y + 1) Combine like terms: 6y + 20y = 26y -20 + 26y = 3(y + -2) + -4(2y + 1) Reorder the terms: -20 + 26y = 3(-2 + y) + -4(2y + 1) -20 + 26y = (-2 * 3 + y * 3) + -4(2y + 1) -20 + 26y = (-6 + 3y) + -4(2y + 1) Reorder the terms: -20 + 26y = -6 + 3y + -4(1 + 2y) -20 + 26y = -6 + 3y + (1 * -4 + 2y * -4) -20 + 26y = -6 + 3y + (-4 + -8y) Reorder the terms: -20 + 26y = -6 + -4 + 3y + -8y Combine like terms: -6 + -4 = -10 -20 + 26y = -10 + 3y + -8y Combine like terms: 3y + -8y = -5y -20 + 26y = -10 + -5y Solving -20 + 26y = -10 + -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. -20 + 26y + 5y = -10 + -5y + 5y Combine like terms: 26y + 5y = 31y -20 + 31y = -10 + -5y + 5y Combine like terms: -5y + 5y = 0 -20 + 31y = -10 + 0 -20 + 31y = -10 Add '20' to each side of the equation. -20 + 20 + 31y = -10 + 20 Combine like terms: -20 + 20 = 0 0 + 31y = -10 + 20 31y = -10 + 20 Combine like terms: -10 + 20 = 10 31y = 10 Divide each side by '31'. y = 0.3225806452 Simplifying y = 0.3225806452
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