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Simplifying 8 + -1(2k + 4) = 2[(8k + -4) + -1(k + -7)] Reorder the terms: 8 + -1(4 + 2k) = 2[(8k + -4) + -1(k + -7)] 8 + (4 * -1 + 2k * -1) = 2[(8k + -4) + -1(k + -7)] 8 + (-4 + -2k) = 2[(8k + -4) + -1(k + -7)] Combine like terms: 8 + -4 = 4 4 + -2k = 2[(8k + -4) + -1(k + -7)] Reorder the terms: 4 + -2k = 2[(-4 + 8k) + -1(k + -7)] Remove parenthesis around (-4 + 8k) 4 + -2k = 2[-4 + 8k + -1(k + -7)] Reorder the terms: 4 + -2k = 2[-4 + 8k + -1(-7 + k)] 4 + -2k = 2[-4 + 8k + (-7 * -1 + k * -1)] 4 + -2k = 2[-4 + 8k + (7 + -1k)] Reorder the terms: 4 + -2k = 2[-4 + 7 + 8k + -1k] Combine like terms: -4 + 7 = 3 4 + -2k = 2[3 + 8k + -1k] Combine like terms: 8k + -1k = 7k 4 + -2k = 2[3 + 7k] 4 + -2k = [3 * 2 + 7k * 2] 4 + -2k = [6 + 14k] Solving 4 + -2k = 6 + 14k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-14k' to each side of the equation. 4 + -2k + -14k = 6 + 14k + -14k Combine like terms: -2k + -14k = -16k 4 + -16k = 6 + 14k + -14k Combine like terms: 14k + -14k = 0 4 + -16k = 6 + 0 4 + -16k = 6 Add '-4' to each side of the equation. 4 + -4 + -16k = 6 + -4 Combine like terms: 4 + -4 = 0 0 + -16k = 6 + -4 -16k = 6 + -4 Combine like terms: 6 + -4 = 2 -16k = 2 Divide each side by '-16'. k = -0.125 Simplifying k = -0.125
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