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Simplifying 3(k + -4) = 5(2k + -3) + -2(3k + -5) Reorder the terms: 3(-4 + k) = 5(2k + -3) + -2(3k + -5) (-4 * 3 + k * 3) = 5(2k + -3) + -2(3k + -5) (-12 + 3k) = 5(2k + -3) + -2(3k + -5) Reorder the terms: -12 + 3k = 5(-3 + 2k) + -2(3k + -5) -12 + 3k = (-3 * 5 + 2k * 5) + -2(3k + -5) -12 + 3k = (-15 + 10k) + -2(3k + -5) Reorder the terms: -12 + 3k = -15 + 10k + -2(-5 + 3k) -12 + 3k = -15 + 10k + (-5 * -2 + 3k * -2) -12 + 3k = -15 + 10k + (10 + -6k) Reorder the terms: -12 + 3k = -15 + 10 + 10k + -6k Combine like terms: -15 + 10 = -5 -12 + 3k = -5 + 10k + -6k Combine like terms: 10k + -6k = 4k -12 + 3k = -5 + 4k Solving -12 + 3k = -5 + 4k Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-4k' to each side of the equation. -12 + 3k + -4k = -5 + 4k + -4k Combine like terms: 3k + -4k = -1k -12 + -1k = -5 + 4k + -4k Combine like terms: 4k + -4k = 0 -12 + -1k = -5 + 0 -12 + -1k = -5 Add '12' to each side of the equation. -12 + 12 + -1k = -5 + 12 Combine like terms: -12 + 12 = 0 0 + -1k = -5 + 12 -1k = -5 + 12 Combine like terms: -5 + 12 = 7 -1k = 7 Divide each side by '-1'. k = -7 Simplifying k = -7
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