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Simplifying 8 + -1(4y + 1) = 6[(7y + -1) + -1(y + -3)] Reorder the terms: 8 + -1(1 + 4y) = 6[(7y + -1) + -1(y + -3)] 8 + (1 * -1 + 4y * -1) = 6[(7y + -1) + -1(y + -3)] 8 + (-1 + -4y) = 6[(7y + -1) + -1(y + -3)] Combine like terms: 8 + -1 = 7 7 + -4y = 6[(7y + -1) + -1(y + -3)] Reorder the terms: 7 + -4y = 6[(-1 + 7y) + -1(y + -3)] Remove parenthesis around (-1 + 7y) 7 + -4y = 6[-1 + 7y + -1(y + -3)] Reorder the terms: 7 + -4y = 6[-1 + 7y + -1(-3 + y)] 7 + -4y = 6[-1 + 7y + (-3 * -1 + y * -1)] 7 + -4y = 6[-1 + 7y + (3 + -1y)] Reorder the terms: 7 + -4y = 6[-1 + 3 + 7y + -1y] Combine like terms: -1 + 3 = 2 7 + -4y = 6[2 + 7y + -1y] Combine like terms: 7y + -1y = 6y 7 + -4y = 6[2 + 6y] 7 + -4y = [2 * 6 + 6y * 6] 7 + -4y = [12 + 36y] Solving 7 + -4y = 12 + 36y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-36y' to each side of the equation. 7 + -4y + -36y = 12 + 36y + -36y Combine like terms: -4y + -36y = -40y 7 + -40y = 12 + 36y + -36y Combine like terms: 36y + -36y = 0 7 + -40y = 12 + 0 7 + -40y = 12 Add '-7' to each side of the equation. 7 + -7 + -40y = 12 + -7 Combine like terms: 7 + -7 = 0 0 + -40y = 12 + -7 -40y = 12 + -7 Combine like terms: 12 + -7 = 5 -40y = 5 Divide each side by '-40'. y = -0.125 Simplifying y = -0.125
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