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Simplifying 2(3k + -1) + -4(2k + 2) = 3 + -3(k + 2) Reorder the terms: 2(-1 + 3k) + -4(2k + 2) = 3 + -3(k + 2) (-1 * 2 + 3k * 2) + -4(2k + 2) = 3 + -3(k + 2) (-2 + 6k) + -4(2k + 2) = 3 + -3(k + 2) Reorder the terms: -2 + 6k + -4(2 + 2k) = 3 + -3(k + 2) -2 + 6k + (2 * -4 + 2k * -4) = 3 + -3(k + 2) -2 + 6k + (-8 + -8k) = 3 + -3(k + 2) Reorder the terms: -2 + -8 + 6k + -8k = 3 + -3(k + 2) Combine like terms: -2 + -8 = -10 -10 + 6k + -8k = 3 + -3(k + 2) Combine like terms: 6k + -8k = -2k -10 + -2k = 3 + -3(k + 2) Reorder the terms: -10 + -2k = 3 + -3(2 + k) -10 + -2k = 3 + (2 * -3 + k * -3) -10 + -2k = 3 + (-6 + -3k) Combine like terms: 3 + -6 = -3 -10 + -2k = -3 + -3k Solving -10 + -2k = -3 + -3k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '3k' to each side of the equation. -10 + -2k + 3k = -3 + -3k + 3k Combine like terms: -2k + 3k = 1k -10 + 1k = -3 + -3k + 3k Combine like terms: -3k + 3k = 0 -10 + 1k = -3 + 0 -10 + 1k = -3 Add '10' to each side of the equation. -10 + 10 + 1k = -3 + 10 Combine like terms: -10 + 10 = 0 0 + 1k = -3 + 10 1k = -3 + 10 Combine like terms: -3 + 10 = 7 1k = 7 Divide each side by '1'. k = 7 Simplifying k = 7
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