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Simplifying -19 = 8(n + -1) + 3(-2n + -7) Reorder the terms: -19 = 8(-1 + n) + 3(-2n + -7) -19 = (-1 * 8 + n * 8) + 3(-2n + -7) -19 = (-8 + 8n) + 3(-2n + -7) Reorder the terms: -19 = -8 + 8n + 3(-7 + -2n) -19 = -8 + 8n + (-7 * 3 + -2n * 3) -19 = -8 + 8n + (-21 + -6n) Reorder the terms: -19 = -8 + -21 + 8n + -6n Combine like terms: -8 + -21 = -29 -19 = -29 + 8n + -6n Combine like terms: 8n + -6n = 2n -19 = -29 + 2n Solving -19 = -29 + 2n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2n' to each side of the equation. -19 + -2n = -29 + 2n + -2n Combine like terms: 2n + -2n = 0 -19 + -2n = -29 + 0 -19 + -2n = -29 Add '19' to each side of the equation. -19 + 19 + -2n = -29 + 19 Combine like terms: -19 + 19 = 0 0 + -2n = -29 + 19 -2n = -29 + 19 Combine like terms: -29 + 19 = -10 -2n = -10 Divide each side by '-2'. n = 5 Simplifying n = 5
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