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Simplifying 84 = -10(7 + 10k) + -6(1 + -10k) 84 = (7 * -10 + 10k * -10) + -6(1 + -10k) 84 = (-70 + -100k) + -6(1 + -10k) 84 = -70 + -100k + (1 * -6 + -10k * -6) 84 = -70 + -100k + (-6 + 60k) Reorder the terms: 84 = -70 + -6 + -100k + 60k Combine like terms: -70 + -6 = -76 84 = -76 + -100k + 60k Combine like terms: -100k + 60k = -40k 84 = -76 + -40k Solving 84 = -76 + -40k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '40k' to each side of the equation. 84 + 40k = -76 + -40k + 40k Combine like terms: -40k + 40k = 0 84 + 40k = -76 + 0 84 + 40k = -76 Add '-84' to each side of the equation. 84 + -84 + 40k = -76 + -84 Combine like terms: 84 + -84 = 0 0 + 40k = -76 + -84 40k = -76 + -84 Combine like terms: -76 + -84 = -160 40k = -160 Divide each side by '40'. k = -4 Simplifying k = -4
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