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Simplifying 2(3k + -1) + -3(2k + 1) = 2(5k + -2) + 5 Reorder the terms: 2(-1 + 3k) + -3(2k + 1) = 2(5k + -2) + 5 (-1 * 2 + 3k * 2) + -3(2k + 1) = 2(5k + -2) + 5 (-2 + 6k) + -3(2k + 1) = 2(5k + -2) + 5 Reorder the terms: -2 + 6k + -3(1 + 2k) = 2(5k + -2) + 5 -2 + 6k + (1 * -3 + 2k * -3) = 2(5k + -2) + 5 -2 + 6k + (-3 + -6k) = 2(5k + -2) + 5 Reorder the terms: -2 + -3 + 6k + -6k = 2(5k + -2) + 5 Combine like terms: -2 + -3 = -5 -5 + 6k + -6k = 2(5k + -2) + 5 Combine like terms: 6k + -6k = 0 -5 + 0 = 2(5k + -2) + 5 -5 = 2(5k + -2) + 5 Reorder the terms: -5 = 2(-2 + 5k) + 5 -5 = (-2 * 2 + 5k * 2) + 5 -5 = (-4 + 10k) + 5 Reorder the terms: -5 = -4 + 5 + 10k Combine like terms: -4 + 5 = 1 -5 = 1 + 10k Solving -5 = 1 + 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. -5 + -10k = 1 + 10k + -10k Combine like terms: 10k + -10k = 0 -5 + -10k = 1 + 0 -5 + -10k = 1 Add '5' to each side of the equation. -5 + 5 + -10k = 1 + 5 Combine like terms: -5 + 5 = 0 0 + -10k = 1 + 5 -10k = 1 + 5 Combine like terms: 1 + 5 = 6 -10k = 6 Divide each side by '-10'. k = -0.6 Simplifying k = -0.6
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