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Simplifying 6(2j + 1) + -5 = 7j + 2(j + -1) Reorder the terms: 6(1 + 2j) + -5 = 7j + 2(j + -1) (1 * 6 + 2j * 6) + -5 = 7j + 2(j + -1) (6 + 12j) + -5 = 7j + 2(j + -1) Reorder the terms: 6 + -5 + 12j = 7j + 2(j + -1) Combine like terms: 6 + -5 = 1 1 + 12j = 7j + 2(j + -1) Reorder the terms: 1 + 12j = 7j + 2(-1 + j) 1 + 12j = 7j + (-1 * 2 + j * 2) 1 + 12j = 7j + (-2 + 2j) Reorder the terms: 1 + 12j = -2 + 7j + 2j Combine like terms: 7j + 2j = 9j 1 + 12j = -2 + 9j Solving 1 + 12j = -2 + 9j Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-9j' to each side of the equation. 1 + 12j + -9j = -2 + 9j + -9j Combine like terms: 12j + -9j = 3j 1 + 3j = -2 + 9j + -9j Combine like terms: 9j + -9j = 0 1 + 3j = -2 + 0 1 + 3j = -2 Add '-1' to each side of the equation. 1 + -1 + 3j = -2 + -1 Combine like terms: 1 + -1 = 0 0 + 3j = -2 + -1 3j = -2 + -1 Combine like terms: -2 + -1 = -3 3j = -3 Divide each side by '3'. j = -1 Simplifying j = -1
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