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Simplifying 6(y + 5) = 3[2(2y + -3) + 1] + 5 Reorder the terms: 6(5 + y) = 3[2(2y + -3) + 1] + 5 (5 * 6 + y * 6) = 3[2(2y + -3) + 1] + 5 (30 + 6y) = 3[2(2y + -3) + 1] + 5 Reorder the terms: 30 + 6y = 3[2(-3 + 2y) + 1] + 5 30 + 6y = 3[(-3 * 2 + 2y * 2) + 1] + 5 30 + 6y = 3[(-6 + 4y) + 1] + 5 Reorder the terms: 30 + 6y = 3[-6 + 1 + 4y] + 5 Combine like terms: -6 + 1 = -5 30 + 6y = 3[-5 + 4y] + 5 30 + 6y = [-5 * 3 + 4y * 3] + 5 30 + 6y = [-15 + 12y] + 5 Reorder the terms: 30 + 6y = -15 + 5 + 12y Combine like terms: -15 + 5 = -10 30 + 6y = -10 + 12y Solving 30 + 6y = -10 + 12y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-12y' to each side of the equation. 30 + 6y + -12y = -10 + 12y + -12y Combine like terms: 6y + -12y = -6y 30 + -6y = -10 + 12y + -12y Combine like terms: 12y + -12y = 0 30 + -6y = -10 + 0 30 + -6y = -10 Add '-30' to each side of the equation. 30 + -30 + -6y = -10 + -30 Combine like terms: 30 + -30 = 0 0 + -6y = -10 + -30 -6y = -10 + -30 Combine like terms: -10 + -30 = -40 -6y = -40 Divide each side by '-6'. y = 6.666666667 Simplifying y = 6.666666667
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