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Simplifying -5(5k + 2j) + 2(k + -3j) = 0 Reorder the terms: -5(2j + 5k) + 2(k + -3j) = 0 (2j * -5 + 5k * -5) + 2(k + -3j) = 0 (-10j + -25k) + 2(k + -3j) = 0 Reorder the terms: -10j + -25k + 2(-3j + k) = 0 -10j + -25k + (-3j * 2 + k * 2) = 0 -10j + -25k + (-6j + 2k) = 0 Reorder the terms: -10j + -6j + -25k + 2k = 0 Combine like terms: -10j + -6j = -16j -16j + -25k + 2k = 0 Combine like terms: -25k + 2k = -23k -16j + -23k = 0 Solving -16j + -23k = 0 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '23k' to each side of the equation. -16j + -23k + 23k = 0 + 23k Combine like terms: -23k + 23k = 0 -16j + 0 = 0 + 23k -16j = 0 + 23k Remove the zero: -16j = 23k Divide each side by '-16'. j = -1.4375k Simplifying j = -1.4375k
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