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Simplifying -1(4 + -5z) + -2(-3z + 4) + -3z = -2(6 + -4z + -8(1 + -1z)) (4 * -1 + -5z * -1) + -2(-3z + 4) + -3z = -2(6 + -4z + -8(1 + -1z)) (-4 + 5z) + -2(-3z + 4) + -3z = -2(6 + -4z + -8(1 + -1z)) Reorder the terms: -4 + 5z + -2(4 + -3z) + -3z = -2(6 + -4z + -8(1 + -1z)) -4 + 5z + (4 * -2 + -3z * -2) + -3z = -2(6 + -4z + -8(1 + -1z)) -4 + 5z + (-8 + 6z) + -3z = -2(6 + -4z + -8(1 + -1z)) Reorder the terms: -4 + -8 + 5z + 6z + -3z = -2(6 + -4z + -8(1 + -1z)) Combine like terms: -4 + -8 = -12 -12 + 5z + 6z + -3z = -2(6 + -4z + -8(1 + -1z)) Combine like terms: 5z + 6z = 11z -12 + 11z + -3z = -2(6 + -4z + -8(1 + -1z)) Combine like terms: 11z + -3z = 8z -12 + 8z = -2(6 + -4z + -8(1 + -1z)) -12 + 8z = -2(6 + -4z + (1 * -8 + -1z * -8)) -12 + 8z = -2(6 + -4z + (-8 + 8z)) Reorder the terms: -12 + 8z = -2(6 + -8 + -4z + 8z) Combine like terms: 6 + -8 = -2 -12 + 8z = -2(-2 + -4z + 8z) Combine like terms: -4z + 8z = 4z -12 + 8z = -2(-2 + 4z) -12 + 8z = (-2 * -2 + 4z * -2) -12 + 8z = (4 + -8z) Solving -12 + 8z = 4 + -8z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '8z' to each side of the equation. -12 + 8z + 8z = 4 + -8z + 8z Combine like terms: 8z + 8z = 16z -12 + 16z = 4 + -8z + 8z Combine like terms: -8z + 8z = 0 -12 + 16z = 4 + 0 -12 + 16z = 4 Add '12' to each side of the equation. -12 + 12 + 16z = 4 + 12 Combine like terms: -12 + 12 = 0 0 + 16z = 4 + 12 16z = 4 + 12 Combine like terms: 4 + 12 = 16 16z = 16 Divide each side by '16'. z = 1 Simplifying z = 1
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