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Simplifying 5(6z + -1) + -5(z + 5) = 4(z + 1) Reorder the terms: 5(-1 + 6z) + -5(z + 5) = 4(z + 1) (-1 * 5 + 6z * 5) + -5(z + 5) = 4(z + 1) (-5 + 30z) + -5(z + 5) = 4(z + 1) Reorder the terms: -5 + 30z + -5(5 + z) = 4(z + 1) -5 + 30z + (5 * -5 + z * -5) = 4(z + 1) -5 + 30z + (-25 + -5z) = 4(z + 1) Reorder the terms: -5 + -25 + 30z + -5z = 4(z + 1) Combine like terms: -5 + -25 = -30 -30 + 30z + -5z = 4(z + 1) Combine like terms: 30z + -5z = 25z -30 + 25z = 4(z + 1) Reorder the terms: -30 + 25z = 4(1 + z) -30 + 25z = (1 * 4 + z * 4) -30 + 25z = (4 + 4z) Solving -30 + 25z = 4 + 4z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4z' to each side of the equation. -30 + 25z + -4z = 4 + 4z + -4z Combine like terms: 25z + -4z = 21z -30 + 21z = 4 + 4z + -4z Combine like terms: 4z + -4z = 0 -30 + 21z = 4 + 0 -30 + 21z = 4 Add '30' to each side of the equation. -30 + 30 + 21z = 4 + 30 Combine like terms: -30 + 30 = 0 0 + 21z = 4 + 30 21z = 4 + 30 Combine like terms: 4 + 30 = 34 21z = 34 Divide each side by '21'. z = 1.619047619 Simplifying z = 1.619047619
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