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Simplifying 5(4n + -7) + 1 = 4(7n + -3) + -30 Reorder the terms: 5(-7 + 4n) + 1 = 4(7n + -3) + -30 (-7 * 5 + 4n * 5) + 1 = 4(7n + -3) + -30 (-35 + 20n) + 1 = 4(7n + -3) + -30 Reorder the terms: -35 + 1 + 20n = 4(7n + -3) + -30 Combine like terms: -35 + 1 = -34 -34 + 20n = 4(7n + -3) + -30 Reorder the terms: -34 + 20n = 4(-3 + 7n) + -30 -34 + 20n = (-3 * 4 + 7n * 4) + -30 -34 + 20n = (-12 + 28n) + -30 Reorder the terms: -34 + 20n = -12 + -30 + 28n Combine like terms: -12 + -30 = -42 -34 + 20n = -42 + 28n Solving -34 + 20n = -42 + 28n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-28n' to each side of the equation. -34 + 20n + -28n = -42 + 28n + -28n Combine like terms: 20n + -28n = -8n -34 + -8n = -42 + 28n + -28n Combine like terms: 28n + -28n = 0 -34 + -8n = -42 + 0 -34 + -8n = -42 Add '34' to each side of the equation. -34 + 34 + -8n = -42 + 34 Combine like terms: -34 + 34 = 0 0 + -8n = -42 + 34 -8n = -42 + 34 Combine like terms: -42 + 34 = -8 -8n = -8 Divide each side by '-8'. n = 1 Simplifying n = 1
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