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Simplifying 9(3y + -1) + -5(y + 3) = 16(y + 1) + -6(-3y + -2) Reorder the terms: 9(-1 + 3y) + -5(y + 3) = 16(y + 1) + -6(-3y + -2) (-1 * 9 + 3y * 9) + -5(y + 3) = 16(y + 1) + -6(-3y + -2) (-9 + 27y) + -5(y + 3) = 16(y + 1) + -6(-3y + -2) Reorder the terms: -9 + 27y + -5(3 + y) = 16(y + 1) + -6(-3y + -2) -9 + 27y + (3 * -5 + y * -5) = 16(y + 1) + -6(-3y + -2) -9 + 27y + (-15 + -5y) = 16(y + 1) + -6(-3y + -2) Reorder the terms: -9 + -15 + 27y + -5y = 16(y + 1) + -6(-3y + -2) Combine like terms: -9 + -15 = -24 -24 + 27y + -5y = 16(y + 1) + -6(-3y + -2) Combine like terms: 27y + -5y = 22y -24 + 22y = 16(y + 1) + -6(-3y + -2) Reorder the terms: -24 + 22y = 16(1 + y) + -6(-3y + -2) -24 + 22y = (1 * 16 + y * 16) + -6(-3y + -2) -24 + 22y = (16 + 16y) + -6(-3y + -2) Reorder the terms: -24 + 22y = 16 + 16y + -6(-2 + -3y) -24 + 22y = 16 + 16y + (-2 * -6 + -3y * -6) -24 + 22y = 16 + 16y + (12 + 18y) Reorder the terms: -24 + 22y = 16 + 12 + 16y + 18y Combine like terms: 16 + 12 = 28 -24 + 22y = 28 + 16y + 18y Combine like terms: 16y + 18y = 34y -24 + 22y = 28 + 34y Solving -24 + 22y = 28 + 34y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-34y' to each side of the equation. -24 + 22y + -34y = 28 + 34y + -34y Combine like terms: 22y + -34y = -12y -24 + -12y = 28 + 34y + -34y Combine like terms: 34y + -34y = 0 -24 + -12y = 28 + 0 -24 + -12y = 28 Add '24' to each side of the equation. -24 + 24 + -12y = 28 + 24 Combine like terms: -24 + 24 = 0 0 + -12y = 28 + 24 -12y = 28 + 24 Combine like terms: 28 + 24 = 52 -12y = 52 Divide each side by '-12'. y = -4.333333333 Simplifying y = -4.333333333
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