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Simplifying 12 + -1(3j + -7) = 3j + -1(j + 1) Reorder the terms: 12 + -1(-7 + 3j) = 3j + -1(j + 1) 12 + (-7 * -1 + 3j * -1) = 3j + -1(j + 1) 12 + (7 + -3j) = 3j + -1(j + 1) Combine like terms: 12 + 7 = 19 19 + -3j = 3j + -1(j + 1) Reorder the terms: 19 + -3j = 3j + -1(1 + j) 19 + -3j = 3j + (1 * -1 + j * -1) 19 + -3j = 3j + (-1 + -1j) Reorder the terms: 19 + -3j = -1 + 3j + -1j Combine like terms: 3j + -1j = 2j 19 + -3j = -1 + 2j Solving 19 + -3j = -1 + 2j Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-2j' to each side of the equation. 19 + -3j + -2j = -1 + 2j + -2j Combine like terms: -3j + -2j = -5j 19 + -5j = -1 + 2j + -2j Combine like terms: 2j + -2j = 0 19 + -5j = -1 + 0 19 + -5j = -1 Add '-19' to each side of the equation. 19 + -19 + -5j = -1 + -19 Combine like terms: 19 + -19 = 0 0 + -5j = -1 + -19 -5j = -1 + -19 Combine like terms: -1 + -19 = -20 -5j = -20 Divide each side by '-5'. j = 4 Simplifying j = 4
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