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Simplifying 6 + -1(6k + 1) = 2[(5k + -3) + -1(k + -2)] Reorder the terms: 6 + -1(1 + 6k) = 2[(5k + -3) + -1(k + -2)] 6 + (1 * -1 + 6k * -1) = 2[(5k + -3) + -1(k + -2)] 6 + (-1 + -6k) = 2[(5k + -3) + -1(k + -2)] Combine like terms: 6 + -1 = 5 5 + -6k = 2[(5k + -3) + -1(k + -2)] Reorder the terms: 5 + -6k = 2[(-3 + 5k) + -1(k + -2)] Remove parenthesis around (-3 + 5k) 5 + -6k = 2[-3 + 5k + -1(k + -2)] Reorder the terms: 5 + -6k = 2[-3 + 5k + -1(-2 + k)] 5 + -6k = 2[-3 + 5k + (-2 * -1 + k * -1)] 5 + -6k = 2[-3 + 5k + (2 + -1k)] Reorder the terms: 5 + -6k = 2[-3 + 2 + 5k + -1k] Combine like terms: -3 + 2 = -1 5 + -6k = 2[-1 + 5k + -1k] Combine like terms: 5k + -1k = 4k 5 + -6k = 2[-1 + 4k] 5 + -6k = [-1 * 2 + 4k * 2] 5 + -6k = [-2 + 8k] Solving 5 + -6k = -2 + 8k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-8k' to each side of the equation. 5 + -6k + -8k = -2 + 8k + -8k Combine like terms: -6k + -8k = -14k 5 + -14k = -2 + 8k + -8k Combine like terms: 8k + -8k = 0 5 + -14k = -2 + 0 5 + -14k = -2 Add '-5' to each side of the equation. 5 + -5 + -14k = -2 + -5 Combine like terms: 5 + -5 = 0 0 + -14k = -2 + -5 -14k = -2 + -5 Combine like terms: -2 + -5 = -7 -14k = -7 Divide each side by '-14'. k = 0.5 Simplifying k = 0.5
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