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Simplifying 2(k + -1(4k + 3) + 1) = 2(k + 2) Reorder the terms: 2(k + -1(3 + 4k) + 1) = 2(k + 2) 2(k + (3 * -1 + 4k * -1) + 1) = 2(k + 2) 2(k + (-3 + -4k) + 1) = 2(k + 2) Reorder the terms: 2(-3 + 1 + k + -4k) = 2(k + 2) Combine like terms: -3 + 1 = -2 2(-2 + k + -4k) = 2(k + 2) Combine like terms: k + -4k = -3k 2(-2 + -3k) = 2(k + 2) (-2 * 2 + -3k * 2) = 2(k + 2) (-4 + -6k) = 2(k + 2) Reorder the terms: -4 + -6k = 2(2 + k) -4 + -6k = (2 * 2 + k * 2) -4 + -6k = (4 + 2k) Solving -4 + -6k = 4 + 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. -4 + -6k + -2k = 4 + 2k + -2k Combine like terms: -6k + -2k = -8k -4 + -8k = 4 + 2k + -2k Combine like terms: 2k + -2k = 0 -4 + -8k = 4 + 0 -4 + -8k = 4 Add '4' to each side of the equation. -4 + 4 + -8k = 4 + 4 Combine like terms: -4 + 4 = 0 0 + -8k = 4 + 4 -8k = 4 + 4 Combine like terms: 4 + 4 = 8 -8k = 8 Divide each side by '-8'. k = -1 Simplifying k = -1
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