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Simplifying 2 + 5z = 5(z + 5) + 7(5z + 1) Reorder the terms: 2 + 5z = 5(5 + z) + 7(5z + 1) 2 + 5z = (5 * 5 + z * 5) + 7(5z + 1) 2 + 5z = (25 + 5z) + 7(5z + 1) Reorder the terms: 2 + 5z = 25 + 5z + 7(1 + 5z) 2 + 5z = 25 + 5z + (1 * 7 + 5z * 7) 2 + 5z = 25 + 5z + (7 + 35z) Reorder the terms: 2 + 5z = 25 + 7 + 5z + 35z Combine like terms: 25 + 7 = 32 2 + 5z = 32 + 5z + 35z Combine like terms: 5z + 35z = 40z 2 + 5z = 32 + 40z Solving 2 + 5z = 32 + 40z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-40z' to each side of the equation. 2 + 5z + -40z = 32 + 40z + -40z Combine like terms: 5z + -40z = -35z 2 + -35z = 32 + 40z + -40z Combine like terms: 40z + -40z = 0 2 + -35z = 32 + 0 2 + -35z = 32 Add '-2' to each side of the equation. 2 + -2 + -35z = 32 + -2 Combine like terms: 2 + -2 = 0 0 + -35z = 32 + -2 -35z = 32 + -2 Combine like terms: 32 + -2 = 30 -35z = 30 Divide each side by '-35'. z = -0.8571428571 Simplifying z = -0.8571428571
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