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Simplifying 5(z + -7) + 35 + 3(z + -5) = 35z + 30 Reorder the terms: 5(-7 + z) + 35 + 3(z + -5) = 35z + 30 (-7 * 5 + z * 5) + 35 + 3(z + -5) = 35z + 30 (-35 + 5z) + 35 + 3(z + -5) = 35z + 30 Reorder the terms: -35 + 5z + 35 + 3(-5 + z) = 35z + 30 -35 + 5z + 35 + (-5 * 3 + z * 3) = 35z + 30 -35 + 5z + 35 + (-15 + 3z) = 35z + 30 Reorder the terms: -35 + 35 + -15 + 5z + 3z = 35z + 30 Combine like terms: -35 + 35 = 0 0 + -15 + 5z + 3z = 35z + 30 -15 + 5z + 3z = 35z + 30 Combine like terms: 5z + 3z = 8z -15 + 8z = 35z + 30 Reorder the terms: -15 + 8z = 30 + 35z Solving -15 + 8z = 30 + 35z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-35z' to each side of the equation. -15 + 8z + -35z = 30 + 35z + -35z Combine like terms: 8z + -35z = -27z -15 + -27z = 30 + 35z + -35z Combine like terms: 35z + -35z = 0 -15 + -27z = 30 + 0 -15 + -27z = 30 Add '15' to each side of the equation. -15 + 15 + -27z = 30 + 15 Combine like terms: -15 + 15 = 0 0 + -27z = 30 + 15 -27z = 30 + 15 Combine like terms: 30 + 15 = 45 -27z = 45 Divide each side by '-27'. z = -1.666666667 Simplifying z = -1.666666667
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