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Simplifying 31 + -11(2n + 3) = 6(7n + 2) + -29n Reorder the terms: 31 + -11(3 + 2n) = 6(7n + 2) + -29n 31 + (3 * -11 + 2n * -11) = 6(7n + 2) + -29n 31 + (-33 + -22n) = 6(7n + 2) + -29n Combine like terms: 31 + -33 = -2 -2 + -22n = 6(7n + 2) + -29n Reorder the terms: -2 + -22n = 6(2 + 7n) + -29n -2 + -22n = (2 * 6 + 7n * 6) + -29n -2 + -22n = (12 + 42n) + -29n Combine like terms: 42n + -29n = 13n -2 + -22n = 12 + 13n Solving -2 + -22n = 12 + 13n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-13n' to each side of the equation. -2 + -22n + -13n = 12 + 13n + -13n Combine like terms: -22n + -13n = -35n -2 + -35n = 12 + 13n + -13n Combine like terms: 13n + -13n = 0 -2 + -35n = 12 + 0 -2 + -35n = 12 Add '2' to each side of the equation. -2 + 2 + -35n = 12 + 2 Combine like terms: -2 + 2 = 0 0 + -35n = 12 + 2 -35n = 12 + 2 Combine like terms: 12 + 2 = 14 -35n = 14 Divide each side by '-35'. n = -0.4 Simplifying n = -0.4
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