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Simplifying 2(4z + -1) + -3(z + 2) = 2(z + 1) Reorder the terms: 2(-1 + 4z) + -3(z + 2) = 2(z + 1) (-1 * 2 + 4z * 2) + -3(z + 2) = 2(z + 1) (-2 + 8z) + -3(z + 2) = 2(z + 1) Reorder the terms: -2 + 8z + -3(2 + z) = 2(z + 1) -2 + 8z + (2 * -3 + z * -3) = 2(z + 1) -2 + 8z + (-6 + -3z) = 2(z + 1) Reorder the terms: -2 + -6 + 8z + -3z = 2(z + 1) Combine like terms: -2 + -6 = -8 -8 + 8z + -3z = 2(z + 1) Combine like terms: 8z + -3z = 5z -8 + 5z = 2(z + 1) Reorder the terms: -8 + 5z = 2(1 + z) -8 + 5z = (1 * 2 + z * 2) -8 + 5z = (2 + 2z) Solving -8 + 5z = 2 + 2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2z' to each side of the equation. -8 + 5z + -2z = 2 + 2z + -2z Combine like terms: 5z + -2z = 3z -8 + 3z = 2 + 2z + -2z Combine like terms: 2z + -2z = 0 -8 + 3z = 2 + 0 -8 + 3z = 2 Add '8' to each side of the equation. -8 + 8 + 3z = 2 + 8 Combine like terms: -8 + 8 = 0 0 + 3z = 2 + 8 3z = 2 + 8 Combine like terms: 2 + 8 = 10 3z = 10 Divide each side by '3'. z = 3.333333333 Simplifying z = 3.333333333
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