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Simplifying 5(2z + -1) + -5(z + 7) = 3(z + 1) Reorder the terms: 5(-1 + 2z) + -5(z + 7) = 3(z + 1) (-1 * 5 + 2z * 5) + -5(z + 7) = 3(z + 1) (-5 + 10z) + -5(z + 7) = 3(z + 1) Reorder the terms: -5 + 10z + -5(7 + z) = 3(z + 1) -5 + 10z + (7 * -5 + z * -5) = 3(z + 1) -5 + 10z + (-35 + -5z) = 3(z + 1) Reorder the terms: -5 + -35 + 10z + -5z = 3(z + 1) Combine like terms: -5 + -35 = -40 -40 + 10z + -5z = 3(z + 1) Combine like terms: 10z + -5z = 5z -40 + 5z = 3(z + 1) Reorder the terms: -40 + 5z = 3(1 + z) -40 + 5z = (1 * 3 + z * 3) -40 + 5z = (3 + 3z) Solving -40 + 5z = 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. -40 + 5z + -3z = 3 + 3z + -3z Combine like terms: 5z + -3z = 2z -40 + 2z = 3 + 3z + -3z Combine like terms: 3z + -3z = 0 -40 + 2z = 3 + 0 -40 + 2z = 3 Add '40' to each side of the equation. -40 + 40 + 2z = 3 + 40 Combine like terms: -40 + 40 = 0 0 + 2z = 3 + 40 2z = 3 + 40 Combine like terms: 3 + 40 = 43 2z = 43 Divide each side by '2'. z = 21.5 Simplifying z = 21.5
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