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Simplifying 0.3j + 1.8 = 0.4(j + 5) + -0.2 Reorder the terms: 1.8 + 0.3j = 0.4(j + 5) + -0.2 Reorder the terms: 1.8 + 0.3j = 0.4(5 + j) + -0.2 1.8 + 0.3j = (5 * 0.4 + j * 0.4) + -0.2 1.8 + 0.3j = (2 + 0.4j) + -0.2 Reorder the terms: 1.8 + 0.3j = 2 + -0.2 + 0.4j Combine like terms: 2 + -0.2 = 1.8 1.8 + 0.3j = 1.8 + 0.4j Add '-1.8' to each side of the equation. 1.8 + -1.8 + 0.3j = 1.8 + -1.8 + 0.4j Combine like terms: 1.8 + -1.8 = 0.0 0.0 + 0.3j = 1.8 + -1.8 + 0.4j 0.3j = 1.8 + -1.8 + 0.4j Combine like terms: 1.8 + -1.8 = 0.0 0.3j = 0.0 + 0.4j 0.3j = 0.4j Solving 0.3j = 0.4j Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-0.4j' to each side of the equation. 0.3j + -0.4j = 0.4j + -0.4j Combine like terms: 0.3j + -0.4j = -0.1j -0.1j = 0.4j + -0.4j Combine like terms: 0.4j + -0.4j = 0.0 -0.1j = 0.0 Divide each side by '-0.1'. j = 0 Simplifying j = 0
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