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Simplifying 3[7 + -5(1 + -1n)] + 8n = -16 + 3[61(n + 1)] + -3n 3[7 + (1 * -5 + -1n * -5)] + 8n = -16 + 3[61(n + 1)] + -3n 3[7 + (-5 + 5n)] + 8n = -16 + 3[61(n + 1)] + -3n Combine like terms: 7 + -5 = 2 3[2 + 5n] + 8n = -16 + 3[61(n + 1)] + -3n [2 * 3 + 5n * 3] + 8n = -16 + 3[61(n + 1)] + -3n [6 + 15n] + 8n = -16 + 3[61(n + 1)] + -3n Combine like terms: 15n + 8n = 23n 6 + 23n = -16 + 3[61(n + 1)] + -3n Reorder the terms: 6 + 23n = -16 + 3[61(1 + n)] + -3n 6 + 23n = -16 + 3[(1 * 61 + n * 61)] + -3n 6 + 23n = -16 + 3[(61 + 61n)] + -3n 6 + 23n = -16 + [61 * 3 + 61n * 3] + -3n 6 + 23n = -16 + [183 + 183n] + -3n Combine like terms: -16 + 183 = 167 6 + 23n = 167 + 183n + -3n Combine like terms: 183n + -3n = 180n 6 + 23n = 167 + 180n Solving 6 + 23n = 167 + 180n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-180n' to each side of the equation. 6 + 23n + -180n = 167 + 180n + -180n Combine like terms: 23n + -180n = -157n 6 + -157n = 167 + 180n + -180n Combine like terms: 180n + -180n = 0 6 + -157n = 167 + 0 6 + -157n = 167 Add '-6' to each side of the equation. 6 + -6 + -157n = 167 + -6 Combine like terms: 6 + -6 = 0 0 + -157n = 167 + -6 -157n = 167 + -6 Combine like terms: 167 + -6 = 161 -157n = 161 Divide each side by '-157'. n = -1.025477707 Simplifying n = -1.025477707
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