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Simplifying 3(3n + -7) + -5(8 + -6n) = 5 + 8n + 8n + 3 Reorder the terms: 3(-7 + 3n) + -5(8 + -6n) = 5 + 8n + 8n + 3 (-7 * 3 + 3n * 3) + -5(8 + -6n) = 5 + 8n + 8n + 3 (-21 + 9n) + -5(8 + -6n) = 5 + 8n + 8n + 3 -21 + 9n + (8 * -5 + -6n * -5) = 5 + 8n + 8n + 3 -21 + 9n + (-40 + 30n) = 5 + 8n + 8n + 3 Reorder the terms: -21 + -40 + 9n + 30n = 5 + 8n + 8n + 3 Combine like terms: -21 + -40 = -61 -61 + 9n + 30n = 5 + 8n + 8n + 3 Combine like terms: 9n + 30n = 39n -61 + 39n = 5 + 8n + 8n + 3 Reorder the terms: -61 + 39n = 5 + 3 + 8n + 8n Combine like terms: 5 + 3 = 8 -61 + 39n = 8 + 8n + 8n Combine like terms: 8n + 8n = 16n -61 + 39n = 8 + 16n Solving -61 + 39n = 8 + 16n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-16n' to each side of the equation. -61 + 39n + -16n = 8 + 16n + -16n Combine like terms: 39n + -16n = 23n -61 + 23n = 8 + 16n + -16n Combine like terms: 16n + -16n = 0 -61 + 23n = 8 + 0 -61 + 23n = 8 Add '61' to each side of the equation. -61 + 61 + 23n = 8 + 61 Combine like terms: -61 + 61 = 0 0 + 23n = 8 + 61 23n = 8 + 61 Combine like terms: 8 + 61 = 69 23n = 69 Divide each side by '23'. n = 3 Simplifying n = 3
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