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Simplifying 5(3z + -1) + -4(z + 5) = 4(z + 1) Reorder the terms: 5(-1 + 3z) + -4(z + 5) = 4(z + 1) (-1 * 5 + 3z * 5) + -4(z + 5) = 4(z + 1) (-5 + 15z) + -4(z + 5) = 4(z + 1) Reorder the terms: -5 + 15z + -4(5 + z) = 4(z + 1) -5 + 15z + (5 * -4 + z * -4) = 4(z + 1) -5 + 15z + (-20 + -4z) = 4(z + 1) Reorder the terms: -5 + -20 + 15z + -4z = 4(z + 1) Combine like terms: -5 + -20 = -25 -25 + 15z + -4z = 4(z + 1) Combine like terms: 15z + -4z = 11z -25 + 11z = 4(z + 1) Reorder the terms: -25 + 11z = 4(1 + z) -25 + 11z = (1 * 4 + z * 4) -25 + 11z = (4 + 4z) Solving -25 + 11z = 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. -25 + 11z + -4z = 4 + 4z + -4z Combine like terms: 11z + -4z = 7z -25 + 7z = 4 + 4z + -4z Combine like terms: 4z + -4z = 0 -25 + 7z = 4 + 0 -25 + 7z = 4 Add '25' to each side of the equation. -25 + 25 + 7z = 4 + 25 Combine like terms: -25 + 25 = 0 0 + 7z = 4 + 25 7z = 4 + 25 Combine like terms: 4 + 25 = 29 7z = 29 Divide each side by '7'. z = 4.142857143 Simplifying z = 4.142857143
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