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Simplifying 978 = 31(j + 27) + 17 Reorder the terms: 978 = 31(27 + j) + 17 978 = (27 * 31 + j * 31) + 17 978 = (837 + 31j) + 17 Reorder the terms: 978 = 837 + 17 + 31j Combine like terms: 837 + 17 = 854 978 = 854 + 31j Solving 978 = 854 + 31j Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-31j' to each side of the equation. 978 + -31j = 854 + 31j + -31j Combine like terms: 31j + -31j = 0 978 + -31j = 854 + 0 978 + -31j = 854 Add '-978' to each side of the equation. 978 + -978 + -31j = 854 + -978 Combine like terms: 978 + -978 = 0 0 + -31j = 854 + -978 -31j = 854 + -978 Combine like terms: 854 + -978 = -124 -31j = -124 Divide each side by '-31'. j = 4 Simplifying j = 4
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