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Simplifying 2[5 + -1(2n + 10)] + -13 = 3(4 + n) Reorder the terms: 2[5 + -1(10 + 2n)] + -13 = 3(4 + n) 2[5 + (10 * -1 + 2n * -1)] + -13 = 3(4 + n) 2[5 + (-10 + -2n)] + -13 = 3(4 + n) Combine like terms: 5 + -10 = -5 2[-5 + -2n] + -13 = 3(4 + n) [-5 * 2 + -2n * 2] + -13 = 3(4 + n) [-10 + -4n] + -13 = 3(4 + n) Reorder the terms: -10 + -13 + -4n = 3(4 + n) Combine like terms: -10 + -13 = -23 -23 + -4n = 3(4 + n) -23 + -4n = (4 * 3 + n * 3) -23 + -4n = (12 + 3n) Solving -23 + -4n = 12 + 3n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3n' to each side of the equation. -23 + -4n + -3n = 12 + 3n + -3n Combine like terms: -4n + -3n = -7n -23 + -7n = 12 + 3n + -3n Combine like terms: 3n + -3n = 0 -23 + -7n = 12 + 0 -23 + -7n = 12 Add '23' to each side of the equation. -23 + 23 + -7n = 12 + 23 Combine like terms: -23 + 23 = 0 0 + -7n = 12 + 23 -7n = 12 + 23 Combine like terms: 12 + 23 = 35 -7n = 35 Divide each side by '-7'. n = -5 Simplifying n = -5
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