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Simplifying 5z + -2(4 + i) = 3z + -1i + 7 5z + (4 * -2 + i * -2) = 3z + -1i + 7 5z + (-8 + -2i) = 3z + -1i + 7 Reorder the terms: -8 + -2i + 5z = 3z + -1i + 7 Reorder the terms: -8 + -2i + 5z = 7 + -1i + 3z Solving -8 + -2i + 5z = 7 + -1i + 3z Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add 'i' to each side of the equation. -8 + -2i + i + 5z = 7 + -1i + i + 3z Combine like terms: -2i + i = -1i -8 + -1i + 5z = 7 + -1i + i + 3z Combine like terms: -1i + i = 0 -8 + -1i + 5z = 7 + 0 + 3z -8 + -1i + 5z = 7 + 3z Add '8' to each side of the equation. -8 + -1i + 8 + 5z = 7 + 8 + 3z Reorder the terms: -8 + 8 + -1i + 5z = 7 + 8 + 3z Combine like terms: -8 + 8 = 0 0 + -1i + 5z = 7 + 8 + 3z -1i + 5z = 7 + 8 + 3z Combine like terms: 7 + 8 = 15 -1i + 5z = 15 + 3z Add '-5z' to each side of the equation. -1i + 5z + -5z = 15 + 3z + -5z Combine like terms: 5z + -5z = 0 -1i + 0 = 15 + 3z + -5z -1i = 15 + 3z + -5z Combine like terms: 3z + -5z = -2z -1i = 15 + -2z Divide each side by '-1'. i = -15 + 2z Simplifying i = -15 + 2z
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