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Simplifying 2(4z + -1) + -3(z + 7) = 2(z + 1) Reorder the terms: 2(-1 + 4z) + -3(z + 7) = 2(z + 1) (-1 * 2 + 4z * 2) + -3(z + 7) = 2(z + 1) (-2 + 8z) + -3(z + 7) = 2(z + 1) Reorder the terms: -2 + 8z + -3(7 + z) = 2(z + 1) -2 + 8z + (7 * -3 + z * -3) = 2(z + 1) -2 + 8z + (-21 + -3z) = 2(z + 1) Reorder the terms: -2 + -21 + 8z + -3z = 2(z + 1) Combine like terms: -2 + -21 = -23 -23 + 8z + -3z = 2(z + 1) Combine like terms: 8z + -3z = 5z -23 + 5z = 2(z + 1) Reorder the terms: -23 + 5z = 2(1 + z) -23 + 5z = (1 * 2 + z * 2) -23 + 5z = (2 + 2z) Solving -23 + 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. -23 + 5z + -2z = 2 + 2z + -2z Combine like terms: 5z + -2z = 3z -23 + 3z = 2 + 2z + -2z Combine like terms: 2z + -2z = 0 -23 + 3z = 2 + 0 -23 + 3z = 2 Add '23' to each side of the equation. -23 + 23 + 3z = 2 + 23 Combine like terms: -23 + 23 = 0 0 + 3z = 2 + 23 3z = 2 + 23 Combine like terms: 2 + 23 = 25 3z = 25 Divide each side by '3'. z = 8.333333333 Simplifying z = 8.333333333
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