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Simplifying 3(i + -3) + -7(i + 3) = 4(2i + -3) + -8(2i + 3) Reorder the terms: 3(-3 + i) + -7(i + 3) = 4(2i + -3) + -8(2i + 3) (-3 * 3 + i * 3) + -7(i + 3) = 4(2i + -3) + -8(2i + 3) (-9 + 3i) + -7(i + 3) = 4(2i + -3) + -8(2i + 3) Reorder the terms: -9 + 3i + -7(3 + i) = 4(2i + -3) + -8(2i + 3) -9 + 3i + (3 * -7 + i * -7) = 4(2i + -3) + -8(2i + 3) -9 + 3i + (-21 + -7i) = 4(2i + -3) + -8(2i + 3) Reorder the terms: -9 + -21 + 3i + -7i = 4(2i + -3) + -8(2i + 3) Combine like terms: -9 + -21 = -30 -30 + 3i + -7i = 4(2i + -3) + -8(2i + 3) Combine like terms: 3i + -7i = -4i -30 + -4i = 4(2i + -3) + -8(2i + 3) Reorder the terms: -30 + -4i = 4(-3 + 2i) + -8(2i + 3) -30 + -4i = (-3 * 4 + 2i * 4) + -8(2i + 3) -30 + -4i = (-12 + 8i) + -8(2i + 3) Reorder the terms: -30 + -4i = -12 + 8i + -8(3 + 2i) -30 + -4i = -12 + 8i + (3 * -8 + 2i * -8) -30 + -4i = -12 + 8i + (-24 + -16i) Reorder the terms: -30 + -4i = -12 + -24 + 8i + -16i Combine like terms: -12 + -24 = -36 -30 + -4i = -36 + 8i + -16i Combine like terms: 8i + -16i = -8i -30 + -4i = -36 + -8i Solving -30 + -4i = -36 + -8i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '8i' to each side of the equation. -30 + -4i + 8i = -36 + -8i + 8i Combine like terms: -4i + 8i = 4i -30 + 4i = -36 + -8i + 8i Combine like terms: -8i + 8i = 0 -30 + 4i = -36 + 0 -30 + 4i = -36 Add '30' to each side of the equation. -30 + 30 + 4i = -36 + 30 Combine like terms: -30 + 30 = 0 0 + 4i = -36 + 30 4i = -36 + 30 Combine like terms: -36 + 30 = -6 4i = -6 Divide each side by '4'. i = -1.5 Simplifying i = -1.5
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