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Simplifying 5(3z + -1) + -3(z + 7) = 7(z + 1) Reorder the terms: 5(-1 + 3z) + -3(z + 7) = 7(z + 1) (-1 * 5 + 3z * 5) + -3(z + 7) = 7(z + 1) (-5 + 15z) + -3(z + 7) = 7(z + 1) Reorder the terms: -5 + 15z + -3(7 + z) = 7(z + 1) -5 + 15z + (7 * -3 + z * -3) = 7(z + 1) -5 + 15z + (-21 + -3z) = 7(z + 1) Reorder the terms: -5 + -21 + 15z + -3z = 7(z + 1) Combine like terms: -5 + -21 = -26 -26 + 15z + -3z = 7(z + 1) Combine like terms: 15z + -3z = 12z -26 + 12z = 7(z + 1) Reorder the terms: -26 + 12z = 7(1 + z) -26 + 12z = (1 * 7 + z * 7) -26 + 12z = (7 + 7z) Solving -26 + 12z = 7 + 7z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-7z' to each side of the equation. -26 + 12z + -7z = 7 + 7z + -7z Combine like terms: 12z + -7z = 5z -26 + 5z = 7 + 7z + -7z Combine like terms: 7z + -7z = 0 -26 + 5z = 7 + 0 -26 + 5z = 7 Add '26' to each side of the equation. -26 + 26 + 5z = 7 + 26 Combine like terms: -26 + 26 = 0 0 + 5z = 7 + 26 5z = 7 + 26 Combine like terms: 7 + 26 = 33 5z = 33 Divide each side by '5'. z = 6.6 Simplifying z = 6.6
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