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Simplifying 12(n + -1) = 52 + -14(n + -1) Reorder the terms: 12(-1 + n) = 52 + -14(n + -1) (-1 * 12 + n * 12) = 52 + -14(n + -1) (-12 + 12n) = 52 + -14(n + -1) Reorder the terms: -12 + 12n = 52 + -14(-1 + n) -12 + 12n = 52 + (-1 * -14 + n * -14) -12 + 12n = 52 + (14 + -14n) Combine like terms: 52 + 14 = 66 -12 + 12n = 66 + -14n Solving -12 + 12n = 66 + -14n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '14n' to each side of the equation. -12 + 12n + 14n = 66 + -14n + 14n Combine like terms: 12n + 14n = 26n -12 + 26n = 66 + -14n + 14n Combine like terms: -14n + 14n = 0 -12 + 26n = 66 + 0 -12 + 26n = 66 Add '12' to each side of the equation. -12 + 12 + 26n = 66 + 12 Combine like terms: -12 + 12 = 0 0 + 26n = 66 + 12 26n = 66 + 12 Combine like terms: 66 + 12 = 78 26n = 78 Divide each side by '26'. n = 3 Simplifying n = 3
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