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Simplifying 2(3n + -4) + 3(2n + -3) = 3(n + 5) + 4 Reorder the terms: 2(-4 + 3n) + 3(2n + -3) = 3(n + 5) + 4 (-4 * 2 + 3n * 2) + 3(2n + -3) = 3(n + 5) + 4 (-8 + 6n) + 3(2n + -3) = 3(n + 5) + 4 Reorder the terms: -8 + 6n + 3(-3 + 2n) = 3(n + 5) + 4 -8 + 6n + (-3 * 3 + 2n * 3) = 3(n + 5) + 4 -8 + 6n + (-9 + 6n) = 3(n + 5) + 4 Reorder the terms: -8 + -9 + 6n + 6n = 3(n + 5) + 4 Combine like terms: -8 + -9 = -17 -17 + 6n + 6n = 3(n + 5) + 4 Combine like terms: 6n + 6n = 12n -17 + 12n = 3(n + 5) + 4 Reorder the terms: -17 + 12n = 3(5 + n) + 4 -17 + 12n = (5 * 3 + n * 3) + 4 -17 + 12n = (15 + 3n) + 4 Reorder the terms: -17 + 12n = 15 + 4 + 3n Combine like terms: 15 + 4 = 19 -17 + 12n = 19 + 3n Solving -17 + 12n = 19 + 3n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3n' to each side of the equation. -17 + 12n + -3n = 19 + 3n + -3n Combine like terms: 12n + -3n = 9n -17 + 9n = 19 + 3n + -3n Combine like terms: 3n + -3n = 0 -17 + 9n = 19 + 0 -17 + 9n = 19 Add '17' to each side of the equation. -17 + 17 + 9n = 19 + 17 Combine like terms: -17 + 17 = 0 0 + 9n = 19 + 17 9n = 19 + 17 Combine like terms: 19 + 17 = 36 9n = 36 Divide each side by '9'. n = 4 Simplifying n = 4
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