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Simplifying 3j + 42 = 36 + -4j + 9j Reorder the terms: 42 + 3j = 36 + -4j + 9j Combine like terms: -4j + 9j = 5j 42 + 3j = 36 + 5j Solving 42 + 3j = 36 + 5j Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-5j' to each side of the equation. 42 + 3j + -5j = 36 + 5j + -5j Combine like terms: 3j + -5j = -2j 42 + -2j = 36 + 5j + -5j Combine like terms: 5j + -5j = 0 42 + -2j = 36 + 0 42 + -2j = 36 Add '-42' to each side of the equation. 42 + -42 + -2j = 36 + -42 Combine like terms: 42 + -42 = 0 0 + -2j = 36 + -42 -2j = 36 + -42 Combine like terms: 36 + -42 = -6 -2j = -6 Divide each side by '-2'. j = 3 Simplifying j = 3
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