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Simplifying 5(6z + -1) + -2(z + 3) = 21(z + 1) Reorder the terms: 5(-1 + 6z) + -2(z + 3) = 21(z + 1) (-1 * 5 + 6z * 5) + -2(z + 3) = 21(z + 1) (-5 + 30z) + -2(z + 3) = 21(z + 1) Reorder the terms: -5 + 30z + -2(3 + z) = 21(z + 1) -5 + 30z + (3 * -2 + z * -2) = 21(z + 1) -5 + 30z + (-6 + -2z) = 21(z + 1) Reorder the terms: -5 + -6 + 30z + -2z = 21(z + 1) Combine like terms: -5 + -6 = -11 -11 + 30z + -2z = 21(z + 1) Combine like terms: 30z + -2z = 28z -11 + 28z = 21(z + 1) Reorder the terms: -11 + 28z = 21(1 + z) -11 + 28z = (1 * 21 + z * 21) -11 + 28z = (21 + 21z) Solving -11 + 28z = 21 + 21z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-21z' to each side of the equation. -11 + 28z + -21z = 21 + 21z + -21z Combine like terms: 28z + -21z = 7z -11 + 7z = 21 + 21z + -21z Combine like terms: 21z + -21z = 0 -11 + 7z = 21 + 0 -11 + 7z = 21 Add '11' to each side of the equation. -11 + 11 + 7z = 21 + 11 Combine like terms: -11 + 11 = 0 0 + 7z = 21 + 11 7z = 21 + 11 Combine like terms: 21 + 11 = 32 7z = 32 Divide each side by '7'. z = 4.571428571 Simplifying z = 4.571428571
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