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Simplifying 5(y + -7) + -2y = 1 + -3[(4y + 7) + -2(y + -3)] Reorder the terms: 5(-7 + y) + -2y = 1 + -3[(4y + 7) + -2(y + -3)] (-7 * 5 + y * 5) + -2y = 1 + -3[(4y + 7) + -2(y + -3)] (-35 + 5y) + -2y = 1 + -3[(4y + 7) + -2(y + -3)] Combine like terms: 5y + -2y = 3y -35 + 3y = 1 + -3[(4y + 7) + -2(y + -3)] Reorder the terms: -35 + 3y = 1 + -3[(7 + 4y) + -2(y + -3)] Remove parenthesis around (7 + 4y) -35 + 3y = 1 + -3[7 + 4y + -2(y + -3)] Reorder the terms: -35 + 3y = 1 + -3[7 + 4y + -2(-3 + y)] -35 + 3y = 1 + -3[7 + 4y + (-3 * -2 + y * -2)] -35 + 3y = 1 + -3[7 + 4y + (6 + -2y)] Reorder the terms: -35 + 3y = 1 + -3[7 + 6 + 4y + -2y] Combine like terms: 7 + 6 = 13 -35 + 3y = 1 + -3[13 + 4y + -2y] Combine like terms: 4y + -2y = 2y -35 + 3y = 1 + -3[13 + 2y] -35 + 3y = 1 + [13 * -3 + 2y * -3] -35 + 3y = 1 + [-39 + -6y] Combine like terms: 1 + -39 = -38 -35 + 3y = -38 + -6y Solving -35 + 3y = -38 + -6y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6y' to each side of the equation. -35 + 3y + 6y = -38 + -6y + 6y Combine like terms: 3y + 6y = 9y -35 + 9y = -38 + -6y + 6y Combine like terms: -6y + 6y = 0 -35 + 9y = -38 + 0 -35 + 9y = -38 Add '35' to each side of the equation. -35 + 35 + 9y = -38 + 35 Combine like terms: -35 + 35 = 0 0 + 9y = -38 + 35 9y = -38 + 35 Combine like terms: -38 + 35 = -3 9y = -3 Divide each side by '9'. y = -0.3333333333 Simplifying y = -0.3333333333
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