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Simplifying 38n + 29 + -7(5n + -2) = 3 + 4(n + -10) Reorder the terms: 38n + 29 + -7(-2 + 5n) = 3 + 4(n + -10) 38n + 29 + (-2 * -7 + 5n * -7) = 3 + 4(n + -10) 38n + 29 + (14 + -35n) = 3 + 4(n + -10) Reorder the terms: 29 + 14 + 38n + -35n = 3 + 4(n + -10) Combine like terms: 29 + 14 = 43 43 + 38n + -35n = 3 + 4(n + -10) Combine like terms: 38n + -35n = 3n 43 + 3n = 3 + 4(n + -10) Reorder the terms: 43 + 3n = 3 + 4(-10 + n) 43 + 3n = 3 + (-10 * 4 + n * 4) 43 + 3n = 3 + (-40 + 4n) Combine like terms: 3 + -40 = -37 43 + 3n = -37 + 4n Solving 43 + 3n = -37 + 4n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4n' to each side of the equation. 43 + 3n + -4n = -37 + 4n + -4n Combine like terms: 3n + -4n = -1n 43 + -1n = -37 + 4n + -4n Combine like terms: 4n + -4n = 0 43 + -1n = -37 + 0 43 + -1n = -37 Add '-43' to each side of the equation. 43 + -43 + -1n = -37 + -43 Combine like terms: 43 + -43 = 0 0 + -1n = -37 + -43 -1n = -37 + -43 Combine like terms: -37 + -43 = -80 -1n = -80 Divide each side by '-1'. n = 80 Simplifying n = 80
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