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Simplifying 2(5z + -1) + -5(z + 4) = 3(z + 1) Reorder the terms: 2(-1 + 5z) + -5(z + 4) = 3(z + 1) (-1 * 2 + 5z * 2) + -5(z + 4) = 3(z + 1) (-2 + 10z) + -5(z + 4) = 3(z + 1) Reorder the terms: -2 + 10z + -5(4 + z) = 3(z + 1) -2 + 10z + (4 * -5 + z * -5) = 3(z + 1) -2 + 10z + (-20 + -5z) = 3(z + 1) Reorder the terms: -2 + -20 + 10z + -5z = 3(z + 1) Combine like terms: -2 + -20 = -22 -22 + 10z + -5z = 3(z + 1) Combine like terms: 10z + -5z = 5z -22 + 5z = 3(z + 1) Reorder the terms: -22 + 5z = 3(1 + z) -22 + 5z = (1 * 3 + z * 3) -22 + 5z = (3 + 3z) Solving -22 + 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. -22 + 5z + -3z = 3 + 3z + -3z Combine like terms: 5z + -3z = 2z -22 + 2z = 3 + 3z + -3z Combine like terms: 3z + -3z = 0 -22 + 2z = 3 + 0 -22 + 2z = 3 Add '22' to each side of the equation. -22 + 22 + 2z = 3 + 22 Combine like terms: -22 + 22 = 0 0 + 2z = 3 + 22 2z = 3 + 22 Combine like terms: 3 + 22 = 25 2z = 25 Divide each side by '2'. z = 12.5 Simplifying z = 12.5
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