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Simplifying 3(8x + 4) + -9(5 + -10k) = 0 Reorder the terms: 3(4 + 8x) + -9(5 + -10k) = 0 (4 * 3 + 8x * 3) + -9(5 + -10k) = 0 (12 + 24x) + -9(5 + -10k) = 0 12 + 24x + (5 * -9 + -10k * -9) = 0 12 + 24x + (-45 + 90k) = 0 Reorder the terms: 12 + -45 + 90k + 24x = 0 Combine like terms: 12 + -45 = -33 -33 + 90k + 24x = 0 Solving -33 + 90k + 24x = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '33' to each side of the equation. -33 + 90k + 33 + 24x = 0 + 33 Reorder the terms: -33 + 33 + 90k + 24x = 0 + 33 Combine like terms: -33 + 33 = 0 0 + 90k + 24x = 0 + 33 90k + 24x = 0 + 33 Combine like terms: 0 + 33 = 33 90k + 24x = 33 Add '-24x' to each side of the equation. 90k + 24x + -24x = 33 + -24x Combine like terms: 24x + -24x = 0 90k + 0 = 33 + -24x 90k = 33 + -24x Divide each side by '90'. k = 0.3666666667 + -0.2666666667x Simplifying k = 0.3666666667 + -0.2666666667x
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