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Simplifying 3(5z + -1) + -3(z + 7) = 5(z + 1) Reorder the terms: 3(-1 + 5z) + -3(z + 7) = 5(z + 1) (-1 * 3 + 5z * 3) + -3(z + 7) = 5(z + 1) (-3 + 15z) + -3(z + 7) = 5(z + 1) Reorder the terms: -3 + 15z + -3(7 + z) = 5(z + 1) -3 + 15z + (7 * -3 + z * -3) = 5(z + 1) -3 + 15z + (-21 + -3z) = 5(z + 1) Reorder the terms: -3 + -21 + 15z + -3z = 5(z + 1) Combine like terms: -3 + -21 = -24 -24 + 15z + -3z = 5(z + 1) Combine like terms: 15z + -3z = 12z -24 + 12z = 5(z + 1) Reorder the terms: -24 + 12z = 5(1 + z) -24 + 12z = (1 * 5 + z * 5) -24 + 12z = (5 + 5z) Solving -24 + 12z = 5 + 5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5z' to each side of the equation. -24 + 12z + -5z = 5 + 5z + -5z Combine like terms: 12z + -5z = 7z -24 + 7z = 5 + 5z + -5z Combine like terms: 5z + -5z = 0 -24 + 7z = 5 + 0 -24 + 7z = 5 Add '24' to each side of the equation. -24 + 24 + 7z = 5 + 24 Combine like terms: -24 + 24 = 0 0 + 7z = 5 + 24 7z = 5 + 24 Combine like terms: 5 + 24 = 29 7z = 29 Divide each side by '7'. z = 4.142857143 Simplifying z = 4.142857143
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