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Simplifying 6(4z + -1) + -3(z + 8) = 19z + 1 Reorder the terms: 6(-1 + 4z) + -3(z + 8) = 19z + 1 (-1 * 6 + 4z * 6) + -3(z + 8) = 19z + 1 (-6 + 24z) + -3(z + 8) = 19z + 1 Reorder the terms: -6 + 24z + -3(8 + z) = 19z + 1 -6 + 24z + (8 * -3 + z * -3) = 19z + 1 -6 + 24z + (-24 + -3z) = 19z + 1 Reorder the terms: -6 + -24 + 24z + -3z = 19z + 1 Combine like terms: -6 + -24 = -30 -30 + 24z + -3z = 19z + 1 Combine like terms: 24z + -3z = 21z -30 + 21z = 19z + 1 Reorder the terms: -30 + 21z = 1 + 19z Solving -30 + 21z = 1 + 19z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-19z' to each side of the equation. -30 + 21z + -19z = 1 + 19z + -19z Combine like terms: 21z + -19z = 2z -30 + 2z = 1 + 19z + -19z Combine like terms: 19z + -19z = 0 -30 + 2z = 1 + 0 -30 + 2z = 1 Add '30' to each side of the equation. -30 + 30 + 2z = 1 + 30 Combine like terms: -30 + 30 = 0 0 + 2z = 1 + 30 2z = 1 + 30 Combine like terms: 1 + 30 = 31 2z = 31 Divide each side by '2'. z = 15.5 Simplifying z = 15.5
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