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Simplifying -8n + -51 + 2n = 5(5 + -5n) + -3(-3 + 22n) Reorder the terms: -51 + -8n + 2n = 5(5 + -5n) + -3(-3 + 22n) Combine like terms: -8n + 2n = -6n -51 + -6n = 5(5 + -5n) + -3(-3 + 22n) -51 + -6n = (5 * 5 + -5n * 5) + -3(-3 + 22n) -51 + -6n = (25 + -25n) + -3(-3 + 22n) -51 + -6n = 25 + -25n + (-3 * -3 + 22n * -3) -51 + -6n = 25 + -25n + (9 + -66n) Reorder the terms: -51 + -6n = 25 + 9 + -25n + -66n Combine like terms: 25 + 9 = 34 -51 + -6n = 34 + -25n + -66n Combine like terms: -25n + -66n = -91n -51 + -6n = 34 + -91n Solving -51 + -6n = 34 + -91n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '91n' to each side of the equation. -51 + -6n + 91n = 34 + -91n + 91n Combine like terms: -6n + 91n = 85n -51 + 85n = 34 + -91n + 91n Combine like terms: -91n + 91n = 0 -51 + 85n = 34 + 0 -51 + 85n = 34 Add '51' to each side of the equation. -51 + 51 + 85n = 34 + 51 Combine like terms: -51 + 51 = 0 0 + 85n = 34 + 51 85n = 34 + 51 Combine like terms: 34 + 51 = 85 85n = 85 Divide each side by '85'. n = 1 Simplifying n = 1
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