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Simplifying -47 = -5(2n + 3) + 6(n + -2) Reorder the terms: -47 = -5(3 + 2n) + 6(n + -2) -47 = (3 * -5 + 2n * -5) + 6(n + -2) -47 = (-15 + -10n) + 6(n + -2) Reorder the terms: -47 = -15 + -10n + 6(-2 + n) -47 = -15 + -10n + (-2 * 6 + n * 6) -47 = -15 + -10n + (-12 + 6n) Reorder the terms: -47 = -15 + -12 + -10n + 6n Combine like terms: -15 + -12 = -27 -47 = -27 + -10n + 6n Combine like terms: -10n + 6n = -4n -47 = -27 + -4n Solving -47 = -27 + -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. -47 + 4n = -27 + -4n + 4n Combine like terms: -4n + 4n = 0 -47 + 4n = -27 + 0 -47 + 4n = -27 Add '47' to each side of the equation. -47 + 47 + 4n = -27 + 47 Combine like terms: -47 + 47 = 0 0 + 4n = -27 + 47 4n = -27 + 47 Combine like terms: -27 + 47 = 20 4n = 20 Divide each side by '4'. n = 5 Simplifying n = 5
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