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Simplifying 3(2j + -1k) + -4(j + -2k) = 0 (2j * 3 + -1k * 3) + -4(j + -2k) = 0 (6j + -3k) + -4(j + -2k) = 0 6j + -3k + (j * -4 + -2k * -4) = 0 6j + -3k + (-4j + 8k) = 0 Reorder the terms: 6j + -4j + -3k + 8k = 0 Combine like terms: 6j + -4j = 2j 2j + -3k + 8k = 0 Combine like terms: -3k + 8k = 5k 2j + 5k = 0 Solving 2j + 5k = 0 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-5k' to each side of the equation. 2j + 5k + -5k = 0 + -5k Combine like terms: 5k + -5k = 0 2j + 0 = 0 + -5k 2j = 0 + -5k Remove the zero: 2j = -5k Divide each side by '2'. j = -2.5k Simplifying j = -2.5k
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