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Simplifying 3 + -1(4k + 8) = 5[(3k + -8) + -1(k + -6)] Reorder the terms: 3 + -1(8 + 4k) = 5[(3k + -8) + -1(k + -6)] 3 + (8 * -1 + 4k * -1) = 5[(3k + -8) + -1(k + -6)] 3 + (-8 + -4k) = 5[(3k + -8) + -1(k + -6)] Combine like terms: 3 + -8 = -5 -5 + -4k = 5[(3k + -8) + -1(k + -6)] Reorder the terms: -5 + -4k = 5[(-8 + 3k) + -1(k + -6)] Remove parenthesis around (-8 + 3k) -5 + -4k = 5[-8 + 3k + -1(k + -6)] Reorder the terms: -5 + -4k = 5[-8 + 3k + -1(-6 + k)] -5 + -4k = 5[-8 + 3k + (-6 * -1 + k * -1)] -5 + -4k = 5[-8 + 3k + (6 + -1k)] Reorder the terms: -5 + -4k = 5[-8 + 6 + 3k + -1k] Combine like terms: -8 + 6 = -2 -5 + -4k = 5[-2 + 3k + -1k] Combine like terms: 3k + -1k = 2k -5 + -4k = 5[-2 + 2k] -5 + -4k = [-2 * 5 + 2k * 5] -5 + -4k = [-10 + 10k] Solving -5 + -4k = -10 + 10k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-10k' to each side of the equation. -5 + -4k + -10k = -10 + 10k + -10k Combine like terms: -4k + -10k = -14k -5 + -14k = -10 + 10k + -10k Combine like terms: 10k + -10k = 0 -5 + -14k = -10 + 0 -5 + -14k = -10 Add '5' to each side of the equation. -5 + 5 + -14k = -10 + 5 Combine like terms: -5 + 5 = 0 0 + -14k = -10 + 5 -14k = -10 + 5 Combine like terms: -10 + 5 = -5 -14k = -5 Divide each side by '-14'. k = 0.3571428571 Simplifying k = 0.3571428571
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