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Simplifying 53 = 6(n + -2) + -1(-5n + 1) Reorder the terms: 53 = 6(-2 + n) + -1(-5n + 1) 53 = (-2 * 6 + n * 6) + -1(-5n + 1) 53 = (-12 + 6n) + -1(-5n + 1) Reorder the terms: 53 = -12 + 6n + -1(1 + -5n) 53 = -12 + 6n + (1 * -1 + -5n * -1) 53 = -12 + 6n + (-1 + 5n) Reorder the terms: 53 = -12 + -1 + 6n + 5n Combine like terms: -12 + -1 = -13 53 = -13 + 6n + 5n Combine like terms: 6n + 5n = 11n 53 = -13 + 11n Solving 53 = -13 + 11n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-11n' to each side of the equation. 53 + -11n = -13 + 11n + -11n Combine like terms: 11n + -11n = 0 53 + -11n = -13 + 0 53 + -11n = -13 Add '-53' to each side of the equation. 53 + -53 + -11n = -13 + -53 Combine like terms: 53 + -53 = 0 0 + -11n = -13 + -53 -11n = -13 + -53 Combine like terms: -13 + -53 = -66 -11n = -66 Divide each side by '-11'. n = 6 Simplifying n = 6
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