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Simplifying 5(6z + -1) + -5(z + 7) = 8(z + 1) Reorder the terms: 5(-1 + 6z) + -5(z + 7) = 8(z + 1) (-1 * 5 + 6z * 5) + -5(z + 7) = 8(z + 1) (-5 + 30z) + -5(z + 7) = 8(z + 1) Reorder the terms: -5 + 30z + -5(7 + z) = 8(z + 1) -5 + 30z + (7 * -5 + z * -5) = 8(z + 1) -5 + 30z + (-35 + -5z) = 8(z + 1) Reorder the terms: -5 + -35 + 30z + -5z = 8(z + 1) Combine like terms: -5 + -35 = -40 -40 + 30z + -5z = 8(z + 1) Combine like terms: 30z + -5z = 25z -40 + 25z = 8(z + 1) Reorder the terms: -40 + 25z = 8(1 + z) -40 + 25z = (1 * 8 + z * 8) -40 + 25z = (8 + 8z) Solving -40 + 25z = 8 + 8z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-8z' to each side of the equation. -40 + 25z + -8z = 8 + 8z + -8z Combine like terms: 25z + -8z = 17z -40 + 17z = 8 + 8z + -8z Combine like terms: 8z + -8z = 0 -40 + 17z = 8 + 0 -40 + 17z = 8 Add '40' to each side of the equation. -40 + 40 + 17z = 8 + 40 Combine like terms: -40 + 40 = 0 0 + 17z = 8 + 40 17z = 8 + 40 Combine like terms: 8 + 40 = 48 17z = 48 Divide each side by '17'. z = 2.823529412 Simplifying z = 2.823529412
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