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Simplifying 0 = 5(5k + 2) + -2(4k + -3) Reorder the terms: 0 = 5(2 + 5k) + -2(4k + -3) 0 = (2 * 5 + 5k * 5) + -2(4k + -3) 0 = (10 + 25k) + -2(4k + -3) Reorder the terms: 0 = 10 + 25k + -2(-3 + 4k) 0 = 10 + 25k + (-3 * -2 + 4k * -2) 0 = 10 + 25k + (6 + -8k) Reorder the terms: 0 = 10 + 6 + 25k + -8k Combine like terms: 10 + 6 = 16 0 = 16 + 25k + -8k Combine like terms: 25k + -8k = 17k 0 = 16 + 17k Solving 0 = 16 + 17k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-17k' to each side of the equation. 0 + -17k = 16 + 17k + -17k Remove the zero: -17k = 16 + 17k + -17k Combine like terms: 17k + -17k = 0 -17k = 16 + 0 -17k = 16 Divide each side by '-17'. k = -0.9411764706 Simplifying k = -0.9411764706
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