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Simplifying -2[(-1k + -3)(-2) + -3] = (-3 + -3k)(-8) + -9 Reorder the terms: -2[(-3 + -1k)(-2) + -3] = (-3 + -3k)(-8) + -9 Reorder the terms for easier multiplication: -2[-2(-3 + -1k) + -3] = (-3 + -3k)(-8) + -9 -2[(-3 * -2 + -1k * -2) + -3] = (-3 + -3k)(-8) + -9 -2[(6 + 2k) + -3] = (-3 + -3k)(-8) + -9 Reorder the terms: -2[6 + -3 + 2k] = (-3 + -3k)(-8) + -9 Combine like terms: 6 + -3 = 3 -2[3 + 2k] = (-3 + -3k)(-8) + -9 [3 * -2 + 2k * -2] = (-3 + -3k)(-8) + -9 [-6 + -4k] = (-3 + -3k)(-8) + -9 Reorder the terms for easier multiplication: -6 + -4k = -8(-3 + -3k) + -9 -6 + -4k = (-3 * -8 + -3k * -8) + -9 -6 + -4k = (24 + 24k) + -9 Reorder the terms: -6 + -4k = 24 + -9 + 24k Combine like terms: 24 + -9 = 15 -6 + -4k = 15 + 24k Solving -6 + -4k = 15 + 24k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-24k' to each side of the equation. -6 + -4k + -24k = 15 + 24k + -24k Combine like terms: -4k + -24k = -28k -6 + -28k = 15 + 24k + -24k Combine like terms: 24k + -24k = 0 -6 + -28k = 15 + 0 -6 + -28k = 15 Add '6' to each side of the equation. -6 + 6 + -28k = 15 + 6 Combine like terms: -6 + 6 = 0 0 + -28k = 15 + 6 -28k = 15 + 6 Combine like terms: 15 + 6 = 21 -28k = 21 Divide each side by '-28'. k = -0.75 Simplifying k = -0.75
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