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Simplifying 14(0.3n + 0.31) = 5.18 + -1(0.4 + -4.22n) Reorder the terms: 14(0.31 + 0.3n) = 5.18 + -1(0.4 + -4.22n) (0.31 * 14 + 0.3n * 14) = 5.18 + -1(0.4 + -4.22n) (4.34 + 4.2n) = 5.18 + -1(0.4 + -4.22n) 4.34 + 4.2n = 5.18 + (0.4 * -1 + -4.22n * -1) 4.34 + 4.2n = 5.18 + (-0.4 + 4.22n) Combine like terms: 5.18 + -0.4 = 4.78 4.34 + 4.2n = 4.78 + 4.22n Solving 4.34 + 4.2n = 4.78 + 4.22n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4.22n' to each side of the equation. 4.34 + 4.2n + -4.22n = 4.78 + 4.22n + -4.22n Combine like terms: 4.2n + -4.22n = -0.02n 4.34 + -0.02n = 4.78 + 4.22n + -4.22n Combine like terms: 4.22n + -4.22n = 0.00 4.34 + -0.02n = 4.78 + 0.00 4.34 + -0.02n = 4.78 Add '-4.34' to each side of the equation. 4.34 + -4.34 + -0.02n = 4.78 + -4.34 Combine like terms: 4.34 + -4.34 = 0.00 0.00 + -0.02n = 4.78 + -4.34 -0.02n = 4.78 + -4.34 Combine like terms: 4.78 + -4.34 = 0.44 -0.02n = 0.44 Divide each side by '-0.02'. n = -22 Simplifying n = -22
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