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Simplifying 5(6z + -1) + -3(z + 7) = 19(z + 1) Reorder the terms: 5(-1 + 6z) + -3(z + 7) = 19(z + 1) (-1 * 5 + 6z * 5) + -3(z + 7) = 19(z + 1) (-5 + 30z) + -3(z + 7) = 19(z + 1) Reorder the terms: -5 + 30z + -3(7 + z) = 19(z + 1) -5 + 30z + (7 * -3 + z * -3) = 19(z + 1) -5 + 30z + (-21 + -3z) = 19(z + 1) Reorder the terms: -5 + -21 + 30z + -3z = 19(z + 1) Combine like terms: -5 + -21 = -26 -26 + 30z + -3z = 19(z + 1) Combine like terms: 30z + -3z = 27z -26 + 27z = 19(z + 1) Reorder the terms: -26 + 27z = 19(1 + z) -26 + 27z = (1 * 19 + z * 19) -26 + 27z = (19 + 19z) Solving -26 + 27z = 19 + 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. -26 + 27z + -19z = 19 + 19z + -19z Combine like terms: 27z + -19z = 8z -26 + 8z = 19 + 19z + -19z Combine like terms: 19z + -19z = 0 -26 + 8z = 19 + 0 -26 + 8z = 19 Add '26' to each side of the equation. -26 + 26 + 8z = 19 + 26 Combine like terms: -26 + 26 = 0 0 + 8z = 19 + 26 8z = 19 + 26 Combine like terms: 19 + 26 = 45 8z = 45 Divide each side by '8'. z = 5.625 Simplifying z = 5.625
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