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Simplifying 2(4z + -1) + -2(z + 4) = 3(z + 1) Reorder the terms: 2(-1 + 4z) + -2(z + 4) = 3(z + 1) (-1 * 2 + 4z * 2) + -2(z + 4) = 3(z + 1) (-2 + 8z) + -2(z + 4) = 3(z + 1) Reorder the terms: -2 + 8z + -2(4 + z) = 3(z + 1) -2 + 8z + (4 * -2 + z * -2) = 3(z + 1) -2 + 8z + (-8 + -2z) = 3(z + 1) Reorder the terms: -2 + -8 + 8z + -2z = 3(z + 1) Combine like terms: -2 + -8 = -10 -10 + 8z + -2z = 3(z + 1) Combine like terms: 8z + -2z = 6z -10 + 6z = 3(z + 1) Reorder the terms: -10 + 6z = 3(1 + z) -10 + 6z = (1 * 3 + z * 3) -10 + 6z = (3 + 3z) Solving -10 + 6z = 3 + 3z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3z' to each side of the equation. -10 + 6z + -3z = 3 + 3z + -3z Combine like terms: 6z + -3z = 3z -10 + 3z = 3 + 3z + -3z Combine like terms: 3z + -3z = 0 -10 + 3z = 3 + 0 -10 + 3z = 3 Add '10' to each side of the equation. -10 + 10 + 3z = 3 + 10 Combine like terms: -10 + 10 = 0 0 + 3z = 3 + 10 3z = 3 + 10 Combine like terms: 3 + 10 = 13 3z = 13 Divide each side by '3'. z = 4.333333333 Simplifying z = 4.333333333
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