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Simplifying 14(0.3n + 0.32) = 5.67 + -1(0.5 + -4.23n) Reorder the terms: 14(0.32 + 0.3n) = 5.67 + -1(0.5 + -4.23n) (0.32 * 14 + 0.3n * 14) = 5.67 + -1(0.5 + -4.23n) (4.48 + 4.2n) = 5.67 + -1(0.5 + -4.23n) 4.48 + 4.2n = 5.67 + (0.5 * -1 + -4.23n * -1) 4.48 + 4.2n = 5.67 + (-0.5 + 4.23n) Combine like terms: 5.67 + -0.5 = 5.17 4.48 + 4.2n = 5.17 + 4.23n Solving 4.48 + 4.2n = 5.17 + 4.23n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4.23n' to each side of the equation. 4.48 + 4.2n + -4.23n = 5.17 + 4.23n + -4.23n Combine like terms: 4.2n + -4.23n = -0.03n 4.48 + -0.03n = 5.17 + 4.23n + -4.23n Combine like terms: 4.23n + -4.23n = 0.00 4.48 + -0.03n = 5.17 + 0.00 4.48 + -0.03n = 5.17 Add '-4.48' to each side of the equation. 4.48 + -4.48 + -0.03n = 5.17 + -4.48 Combine like terms: 4.48 + -4.48 = 0.00 0.00 + -0.03n = 5.17 + -4.48 -0.03n = 5.17 + -4.48 Combine like terms: 5.17 + -4.48 = 0.69 -0.03n = 0.69 Divide each side by '-0.03'. n = -23 Simplifying n = -23
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