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Simplifying 5 + -1(6k + 1) = 2[(5k + -3) + -1(5 + -2)] Reorder the terms: 5 + -1(1 + 6k) = 2[(5k + -3) + -1(5 + -2)] 5 + (1 * -1 + 6k * -1) = 2[(5k + -3) + -1(5 + -2)] 5 + (-1 + -6k) = 2[(5k + -3) + -1(5 + -2)] Combine like terms: 5 + -1 = 4 4 + -6k = 2[(5k + -3) + -1(5 + -2)] Reorder the terms: 4 + -6k = 2[(-3 + 5k) + -1(5 + -2)] Remove parenthesis around (-3 + 5k) 4 + -6k = 2[-3 + 5k + -1(5 + -2)] Combine like terms: 5 + -2 = 3 4 + -6k = 2[-3 + 5k + -1(3)] Multiply -1 * 3 4 + -6k = 2[-3 + 5k + -3] Reorder the terms: 4 + -6k = 2[-3 + -3 + 5k] Combine like terms: -3 + -3 = -6 4 + -6k = 2[-6 + 5k] 4 + -6k = [-6 * 2 + 5k * 2] 4 + -6k = [-12 + 10k] Solving 4 + -6k = -12 + 10k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-10k' to each side of the equation. 4 + -6k + -10k = -12 + 10k + -10k Combine like terms: -6k + -10k = -16k 4 + -16k = -12 + 10k + -10k Combine like terms: 10k + -10k = 0 4 + -16k = -12 + 0 4 + -16k = -12 Add '-4' to each side of the equation. 4 + -4 + -16k = -12 + -4 Combine like terms: 4 + -4 = 0 0 + -16k = -12 + -4 -16k = -12 + -4 Combine like terms: -12 + -4 = -16 -16k = -16 Divide each side by '-16'. k = 1 Simplifying k = 1
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