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Simplifying -2[4(k + -2) + -3(k + 1)] = 14 + 2k Reorder the terms: -2[4(-2 + k) + -3(k + 1)] = 14 + 2k -2[(-2 * 4 + k * 4) + -3(k + 1)] = 14 + 2k -2[(-8 + 4k) + -3(k + 1)] = 14 + 2k Reorder the terms: -2[-8 + 4k + -3(1 + k)] = 14 + 2k -2[-8 + 4k + (1 * -3 + k * -3)] = 14 + 2k -2[-8 + 4k + (-3 + -3k)] = 14 + 2k Reorder the terms: -2[-8 + -3 + 4k + -3k] = 14 + 2k Combine like terms: -8 + -3 = -11 -2[-11 + 4k + -3k] = 14 + 2k Combine like terms: 4k + -3k = 1k -2[-11 + 1k] = 14 + 2k [-11 * -2 + 1k * -2] = 14 + 2k [22 + -2k] = 14 + 2k Solving 22 + -2k = 14 + 2k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2k' to each side of the equation. 22 + -2k + -2k = 14 + 2k + -2k Combine like terms: -2k + -2k = -4k 22 + -4k = 14 + 2k + -2k Combine like terms: 2k + -2k = 0 22 + -4k = 14 + 0 22 + -4k = 14 Add '-22' to each side of the equation. 22 + -22 + -4k = 14 + -22 Combine like terms: 22 + -22 = 0 0 + -4k = 14 + -22 -4k = 14 + -22 Combine like terms: 14 + -22 = -8 -4k = -8 Divide each side by '-4'. k = 2 Simplifying k = 2
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