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Simplifying 7 + -8k + -8k = -9(k + 3) + 5(k + -10) Combine like terms: -8k + -8k = -16k 7 + -16k = -9(k + 3) + 5(k + -10) Reorder the terms: 7 + -16k = -9(3 + k) + 5(k + -10) 7 + -16k = (3 * -9 + k * -9) + 5(k + -10) 7 + -16k = (-27 + -9k) + 5(k + -10) Reorder the terms: 7 + -16k = -27 + -9k + 5(-10 + k) 7 + -16k = -27 + -9k + (-10 * 5 + k * 5) 7 + -16k = -27 + -9k + (-50 + 5k) Reorder the terms: 7 + -16k = -27 + -50 + -9k + 5k Combine like terms: -27 + -50 = -77 7 + -16k = -77 + -9k + 5k Combine like terms: -9k + 5k = -4k 7 + -16k = -77 + -4k Solving 7 + -16k = -77 + -4k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '4k' to each side of the equation. 7 + -16k + 4k = -77 + -4k + 4k Combine like terms: -16k + 4k = -12k 7 + -12k = -77 + -4k + 4k Combine like terms: -4k + 4k = 0 7 + -12k = -77 + 0 7 + -12k = -77 Add '-7' to each side of the equation. 7 + -7 + -12k = -77 + -7 Combine like terms: 7 + -7 = 0 0 + -12k = -77 + -7 -12k = -77 + -7 Combine like terms: -77 + -7 = -84 -12k = -84 Divide each side by '-12'. k = 7 Simplifying k = 7
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