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Simplifying 6 + -1(3k + 7) = 5[(5k + -7) + -1(k + -4)] Reorder the terms: 6 + -1(7 + 3k) = 5[(5k + -7) + -1(k + -4)] 6 + (7 * -1 + 3k * -1) = 5[(5k + -7) + -1(k + -4)] 6 + (-7 + -3k) = 5[(5k + -7) + -1(k + -4)] Combine like terms: 6 + -7 = -1 -1 + -3k = 5[(5k + -7) + -1(k + -4)] Reorder the terms: -1 + -3k = 5[(-7 + 5k) + -1(k + -4)] Remove parenthesis around (-7 + 5k) -1 + -3k = 5[-7 + 5k + -1(k + -4)] Reorder the terms: -1 + -3k = 5[-7 + 5k + -1(-4 + k)] -1 + -3k = 5[-7 + 5k + (-4 * -1 + k * -1)] -1 + -3k = 5[-7 + 5k + (4 + -1k)] Reorder the terms: -1 + -3k = 5[-7 + 4 + 5k + -1k] Combine like terms: -7 + 4 = -3 -1 + -3k = 5[-3 + 5k + -1k] Combine like terms: 5k + -1k = 4k -1 + -3k = 5[-3 + 4k] -1 + -3k = [-3 * 5 + 4k * 5] -1 + -3k = [-15 + 20k] Solving -1 + -3k = -15 + 20k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-20k' to each side of the equation. -1 + -3k + -20k = -15 + 20k + -20k Combine like terms: -3k + -20k = -23k -1 + -23k = -15 + 20k + -20k Combine like terms: 20k + -20k = 0 -1 + -23k = -15 + 0 -1 + -23k = -15 Add '1' to each side of the equation. -1 + 1 + -23k = -15 + 1 Combine like terms: -1 + 1 = 0 0 + -23k = -15 + 1 -23k = -15 + 1 Combine like terms: -15 + 1 = -14 -23k = -14 Divide each side by '-23'. k = 0.6086956522 Simplifying k = 0.6086956522
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