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Simplifying 5n + 7(-6 + -1n) = 4(n + 3) 5n + (-6 * 7 + -1n * 7) = 4(n + 3) 5n + (-42 + -7n) = 4(n + 3) Reorder the terms: -42 + 5n + -7n = 4(n + 3) Combine like terms: 5n + -7n = -2n -42 + -2n = 4(n + 3) Reorder the terms: -42 + -2n = 4(3 + n) -42 + -2n = (3 * 4 + n * 4) -42 + -2n = (12 + 4n) Solving -42 + -2n = 12 + 4n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4n' to each side of the equation. -42 + -2n + -4n = 12 + 4n + -4n Combine like terms: -2n + -4n = -6n -42 + -6n = 12 + 4n + -4n Combine like terms: 4n + -4n = 0 -42 + -6n = 12 + 0 -42 + -6n = 12 Add '42' to each side of the equation. -42 + 42 + -6n = 12 + 42 Combine like terms: -42 + 42 = 0 0 + -6n = 12 + 42 -6n = 12 + 42 Combine like terms: 12 + 42 = 54 -6n = 54 Divide each side by '-6'. n = -9 Simplifying n = -9
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