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Simplifying 3y + 2[5(y + -4) + -2] = 5y + 6(7 + y) + -3 Reorder the terms: 3y + 2[5(-4 + y) + -2] = 5y + 6(7 + y) + -3 3y + 2[(-4 * 5 + y * 5) + -2] = 5y + 6(7 + y) + -3 3y + 2[(-20 + 5y) + -2] = 5y + 6(7 + y) + -3 Reorder the terms: 3y + 2[-20 + -2 + 5y] = 5y + 6(7 + y) + -3 Combine like terms: -20 + -2 = -22 3y + 2[-22 + 5y] = 5y + 6(7 + y) + -3 3y + [-22 * 2 + 5y * 2] = 5y + 6(7 + y) + -3 3y + [-44 + 10y] = 5y + 6(7 + y) + -3 Reorder the terms: -44 + 3y + 10y = 5y + 6(7 + y) + -3 Combine like terms: 3y + 10y = 13y -44 + 13y = 5y + 6(7 + y) + -3 -44 + 13y = 5y + (7 * 6 + y * 6) + -3 -44 + 13y = 5y + (42 + 6y) + -3 Reorder the terms: -44 + 13y = 42 + -3 + 5y + 6y Combine like terms: 42 + -3 = 39 -44 + 13y = 39 + 5y + 6y Combine like terms: 5y + 6y = 11y -44 + 13y = 39 + 11y Solving -44 + 13y = 39 + 11y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-11y' to each side of the equation. -44 + 13y + -11y = 39 + 11y + -11y Combine like terms: 13y + -11y = 2y -44 + 2y = 39 + 11y + -11y Combine like terms: 11y + -11y = 0 -44 + 2y = 39 + 0 -44 + 2y = 39 Add '44' to each side of the equation. -44 + 44 + 2y = 39 + 44 Combine like terms: -44 + 44 = 0 0 + 2y = 39 + 44 2y = 39 + 44 Combine like terms: 39 + 44 = 83 2y = 83 Divide each side by '2'. y = 41.5 Simplifying y = 41.5
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