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Simplifying 2(3j + 2) + -4(2j + 3) = 3(2j + -1) + -6(j + 5) Reorder the terms: 2(2 + 3j) + -4(2j + 3) = 3(2j + -1) + -6(j + 5) (2 * 2 + 3j * 2) + -4(2j + 3) = 3(2j + -1) + -6(j + 5) (4 + 6j) + -4(2j + 3) = 3(2j + -1) + -6(j + 5) Reorder the terms: 4 + 6j + -4(3 + 2j) = 3(2j + -1) + -6(j + 5) 4 + 6j + (3 * -4 + 2j * -4) = 3(2j + -1) + -6(j + 5) 4 + 6j + (-12 + -8j) = 3(2j + -1) + -6(j + 5) Reorder the terms: 4 + -12 + 6j + -8j = 3(2j + -1) + -6(j + 5) Combine like terms: 4 + -12 = -8 -8 + 6j + -8j = 3(2j + -1) + -6(j + 5) Combine like terms: 6j + -8j = -2j -8 + -2j = 3(2j + -1) + -6(j + 5) Reorder the terms: -8 + -2j = 3(-1 + 2j) + -6(j + 5) -8 + -2j = (-1 * 3 + 2j * 3) + -6(j + 5) -8 + -2j = (-3 + 6j) + -6(j + 5) Reorder the terms: -8 + -2j = -3 + 6j + -6(5 + j) -8 + -2j = -3 + 6j + (5 * -6 + j * -6) -8 + -2j = -3 + 6j + (-30 + -6j) Reorder the terms: -8 + -2j = -3 + -30 + 6j + -6j Combine like terms: -3 + -30 = -33 -8 + -2j = -33 + 6j + -6j Combine like terms: 6j + -6j = 0 -8 + -2j = -33 + 0 -8 + -2j = -33 Solving -8 + -2j = -33 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -2j = -33 + 8 Combine like terms: -8 + 8 = 0 0 + -2j = -33 + 8 -2j = -33 + 8 Combine like terms: -33 + 8 = -25 -2j = -25 Divide each side by '-2'. j = 12.5 Simplifying j = 12.5
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