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Simplifying 3(4k + -6) + -3(3k + 2) = 2 + -2(k + 2) Reorder the terms: 3(-6 + 4k) + -3(3k + 2) = 2 + -2(k + 2) (-6 * 3 + 4k * 3) + -3(3k + 2) = 2 + -2(k + 2) (-18 + 12k) + -3(3k + 2) = 2 + -2(k + 2) Reorder the terms: -18 + 12k + -3(2 + 3k) = 2 + -2(k + 2) -18 + 12k + (2 * -3 + 3k * -3) = 2 + -2(k + 2) -18 + 12k + (-6 + -9k) = 2 + -2(k + 2) Reorder the terms: -18 + -6 + 12k + -9k = 2 + -2(k + 2) Combine like terms: -18 + -6 = -24 -24 + 12k + -9k = 2 + -2(k + 2) Combine like terms: 12k + -9k = 3k -24 + 3k = 2 + -2(k + 2) Reorder the terms: -24 + 3k = 2 + -2(2 + k) -24 + 3k = 2 + (2 * -2 + k * -2) -24 + 3k = 2 + (-4 + -2k) Combine like terms: 2 + -4 = -2 -24 + 3k = -2 + -2k Solving -24 + 3k = -2 + -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. -24 + 3k + 2k = -2 + -2k + 2k Combine like terms: 3k + 2k = 5k -24 + 5k = -2 + -2k + 2k Combine like terms: -2k + 2k = 0 -24 + 5k = -2 + 0 -24 + 5k = -2 Add '24' to each side of the equation. -24 + 24 + 5k = -2 + 24 Combine like terms: -24 + 24 = 0 0 + 5k = -2 + 24 5k = -2 + 24 Combine like terms: -2 + 24 = 22 5k = 22 Divide each side by '5'. k = 4.4 Simplifying k = 4.4
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