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Simplifying 7(j + 1) + 11 = 5(j + 3) + 9 Reorder the terms: 7(1 + j) + 11 = 5(j + 3) + 9 (1 * 7 + j * 7) + 11 = 5(j + 3) + 9 (7 + 7j) + 11 = 5(j + 3) + 9 Reorder the terms: 7 + 11 + 7j = 5(j + 3) + 9 Combine like terms: 7 + 11 = 18 18 + 7j = 5(j + 3) + 9 Reorder the terms: 18 + 7j = 5(3 + j) + 9 18 + 7j = (3 * 5 + j * 5) + 9 18 + 7j = (15 + 5j) + 9 Reorder the terms: 18 + 7j = 15 + 9 + 5j Combine like terms: 15 + 9 = 24 18 + 7j = 24 + 5j Solving 18 + 7j = 24 + 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. 18 + 7j + -5j = 24 + 5j + -5j Combine like terms: 7j + -5j = 2j 18 + 2j = 24 + 5j + -5j Combine like terms: 5j + -5j = 0 18 + 2j = 24 + 0 18 + 2j = 24 Add '-18' to each side of the equation. 18 + -18 + 2j = 24 + -18 Combine like terms: 18 + -18 = 0 0 + 2j = 24 + -18 2j = 24 + -18 Combine like terms: 24 + -18 = 6 2j = 6 Divide each side by '2'. j = 3 Simplifying j = 3
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