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Simplifying -4(n + -5) + 6(11n + -11) = 1 + 9n + 6n Reorder the terms: -4(-5 + n) + 6(11n + -11) = 1 + 9n + 6n (-5 * -4 + n * -4) + 6(11n + -11) = 1 + 9n + 6n (20 + -4n) + 6(11n + -11) = 1 + 9n + 6n Reorder the terms: 20 + -4n + 6(-11 + 11n) = 1 + 9n + 6n 20 + -4n + (-11 * 6 + 11n * 6) = 1 + 9n + 6n 20 + -4n + (-66 + 66n) = 1 + 9n + 6n Reorder the terms: 20 + -66 + -4n + 66n = 1 + 9n + 6n Combine like terms: 20 + -66 = -46 -46 + -4n + 66n = 1 + 9n + 6n Combine like terms: -4n + 66n = 62n -46 + 62n = 1 + 9n + 6n Combine like terms: 9n + 6n = 15n -46 + 62n = 1 + 15n Solving -46 + 62n = 1 + 15n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-15n' to each side of the equation. -46 + 62n + -15n = 1 + 15n + -15n Combine like terms: 62n + -15n = 47n -46 + 47n = 1 + 15n + -15n Combine like terms: 15n + -15n = 0 -46 + 47n = 1 + 0 -46 + 47n = 1 Add '46' to each side of the equation. -46 + 46 + 47n = 1 + 46 Combine like terms: -46 + 46 = 0 0 + 47n = 1 + 46 47n = 1 + 46 Combine like terms: 1 + 46 = 47 47n = 47 Divide each side by '47'. n = 1 Simplifying n = 1
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