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Simplifying 2(y + -1) + -3(y + -2) + 4(y + -3) = 2(y + 5) Reorder the terms: 2(-1 + y) + -3(y + -2) + 4(y + -3) = 2(y + 5) (-1 * 2 + y * 2) + -3(y + -2) + 4(y + -3) = 2(y + 5) (-2 + 2y) + -3(y + -2) + 4(y + -3) = 2(y + 5) Reorder the terms: -2 + 2y + -3(-2 + y) + 4(y + -3) = 2(y + 5) -2 + 2y + (-2 * -3 + y * -3) + 4(y + -3) = 2(y + 5) -2 + 2y + (6 + -3y) + 4(y + -3) = 2(y + 5) Reorder the terms: -2 + 2y + 6 + -3y + 4(-3 + y) = 2(y + 5) -2 + 2y + 6 + -3y + (-3 * 4 + y * 4) = 2(y + 5) -2 + 2y + 6 + -3y + (-12 + 4y) = 2(y + 5) Reorder the terms: -2 + 6 + -12 + 2y + -3y + 4y = 2(y + 5) Combine like terms: -2 + 6 = 4 4 + -12 + 2y + -3y + 4y = 2(y + 5) Combine like terms: 4 + -12 = -8 -8 + 2y + -3y + 4y = 2(y + 5) Combine like terms: 2y + -3y = -1y -8 + -1y + 4y = 2(y + 5) Combine like terms: -1y + 4y = 3y -8 + 3y = 2(y + 5) Reorder the terms: -8 + 3y = 2(5 + y) -8 + 3y = (5 * 2 + y * 2) -8 + 3y = (10 + 2y) Solving -8 + 3y = 10 + 2y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2y' to each side of the equation. -8 + 3y + -2y = 10 + 2y + -2y Combine like terms: 3y + -2y = 1y -8 + 1y = 10 + 2y + -2y Combine like terms: 2y + -2y = 0 -8 + 1y = 10 + 0 -8 + 1y = 10 Add '8' to each side of the equation. -8 + 8 + 1y = 10 + 8 Combine like terms: -8 + 8 = 0 0 + 1y = 10 + 8 1y = 10 + 8 Combine like terms: 10 + 8 = 18 1y = 18 Divide each side by '1'. y = 18 Simplifying y = 18
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