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Simplifying 2[k + -1(4k + 20) + 10] = 2(k + 10) Reorder the terms: 2[k + -1(20 + 4k) + 10] = 2(k + 10) 2[k + (20 * -1 + 4k * -1) + 10] = 2(k + 10) 2[k + (-20 + -4k) + 10] = 2(k + 10) Reorder the terms: 2[-20 + 10 + k + -4k] = 2(k + 10) Combine like terms: -20 + 10 = -10 2[-10 + k + -4k] = 2(k + 10) Combine like terms: k + -4k = -3k 2[-10 + -3k] = 2(k + 10) [-10 * 2 + -3k * 2] = 2(k + 10) [-20 + -6k] = 2(k + 10) Reorder the terms: -20 + -6k = 2(10 + k) -20 + -6k = (10 * 2 + k * 2) -20 + -6k = (20 + 2k) Solving -20 + -6k = 20 + 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. -20 + -6k + -2k = 20 + 2k + -2k Combine like terms: -6k + -2k = -8k -20 + -8k = 20 + 2k + -2k Combine like terms: 2k + -2k = 0 -20 + -8k = 20 + 0 -20 + -8k = 20 Add '20' to each side of the equation. -20 + 20 + -8k = 20 + 20 Combine like terms: -20 + 20 = 0 0 + -8k = 20 + 20 -8k = 20 + 20 Combine like terms: 20 + 20 = 40 -8k = 40 Divide each side by '-8'. k = -5 Simplifying k = -5
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