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Simplifying 6(5z + -1) + -5(z + 9) = 20(z + 1) Reorder the terms: 6(-1 + 5z) + -5(z + 9) = 20(z + 1) (-1 * 6 + 5z * 6) + -5(z + 9) = 20(z + 1) (-6 + 30z) + -5(z + 9) = 20(z + 1) Reorder the terms: -6 + 30z + -5(9 + z) = 20(z + 1) -6 + 30z + (9 * -5 + z * -5) = 20(z + 1) -6 + 30z + (-45 + -5z) = 20(z + 1) Reorder the terms: -6 + -45 + 30z + -5z = 20(z + 1) Combine like terms: -6 + -45 = -51 -51 + 30z + -5z = 20(z + 1) Combine like terms: 30z + -5z = 25z -51 + 25z = 20(z + 1) Reorder the terms: -51 + 25z = 20(1 + z) -51 + 25z = (1 * 20 + z * 20) -51 + 25z = (20 + 20z) Solving -51 + 25z = 20 + 20z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-20z' to each side of the equation. -51 + 25z + -20z = 20 + 20z + -20z Combine like terms: 25z + -20z = 5z -51 + 5z = 20 + 20z + -20z Combine like terms: 20z + -20z = 0 -51 + 5z = 20 + 0 -51 + 5z = 20 Add '51' to each side of the equation. -51 + 51 + 5z = 20 + 51 Combine like terms: -51 + 51 = 0 0 + 5z = 20 + 51 5z = 20 + 51 Combine like terms: 20 + 51 = 71 5z = 71 Divide each side by '5'. z = 14.2 Simplifying z = 14.2
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