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Simplifying -2(17n + -22) + 6(5n + 3) = n + -1(8n + -38) Reorder the terms: -2(-22 + 17n) + 6(5n + 3) = n + -1(8n + -38) (-22 * -2 + 17n * -2) + 6(5n + 3) = n + -1(8n + -38) (44 + -34n) + 6(5n + 3) = n + -1(8n + -38) Reorder the terms: 44 + -34n + 6(3 + 5n) = n + -1(8n + -38) 44 + -34n + (3 * 6 + 5n * 6) = n + -1(8n + -38) 44 + -34n + (18 + 30n) = n + -1(8n + -38) Reorder the terms: 44 + 18 + -34n + 30n = n + -1(8n + -38) Combine like terms: 44 + 18 = 62 62 + -34n + 30n = n + -1(8n + -38) Combine like terms: -34n + 30n = -4n 62 + -4n = n + -1(8n + -38) Reorder the terms: 62 + -4n = n + -1(-38 + 8n) 62 + -4n = n + (-38 * -1 + 8n * -1) 62 + -4n = n + (38 + -8n) Reorder the terms: 62 + -4n = 38 + n + -8n Combine like terms: n + -8n = -7n 62 + -4n = 38 + -7n Solving 62 + -4n = 38 + -7n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '7n' to each side of the equation. 62 + -4n + 7n = 38 + -7n + 7n Combine like terms: -4n + 7n = 3n 62 + 3n = 38 + -7n + 7n Combine like terms: -7n + 7n = 0 62 + 3n = 38 + 0 62 + 3n = 38 Add '-62' to each side of the equation. 62 + -62 + 3n = 38 + -62 Combine like terms: 62 + -62 = 0 0 + 3n = 38 + -62 3n = 38 + -62 Combine like terms: 38 + -62 = -24 3n = -24 Divide each side by '3'. n = -8 Simplifying n = -8
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