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Simplifying 1(j + 1) = 5(j + -3) Reorder the terms: 1(1 + j) = 5(j + -3) (1 * 1 + j * 1) = 5(j + -3) (1 + 1j) = 5(j + -3) Reorder the terms: 1 + 1j = 5(-3 + j) 1 + 1j = (-3 * 5 + j * 5) 1 + 1j = (-15 + 5j) Solving 1 + 1j = -15 + 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. 1 + 1j + -5j = -15 + 5j + -5j Combine like terms: 1j + -5j = -4j 1 + -4j = -15 + 5j + -5j Combine like terms: 5j + -5j = 0 1 + -4j = -15 + 0 1 + -4j = -15 Add '-1' to each side of the equation. 1 + -1 + -4j = -15 + -1 Combine like terms: 1 + -1 = 0 0 + -4j = -15 + -1 -4j = -15 + -1 Combine like terms: -15 + -1 = -16 -4j = -16 Divide each side by '-4'. j = 4 Simplifying j = 4
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