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Simplifying 5(6z + -1) + -5(z + 9) = 14(z + 1) Reorder the terms: 5(-1 + 6z) + -5(z + 9) = 14(z + 1) (-1 * 5 + 6z * 5) + -5(z + 9) = 14(z + 1) (-5 + 30z) + -5(z + 9) = 14(z + 1) Reorder the terms: -5 + 30z + -5(9 + z) = 14(z + 1) -5 + 30z + (9 * -5 + z * -5) = 14(z + 1) -5 + 30z + (-45 + -5z) = 14(z + 1) Reorder the terms: -5 + -45 + 30z + -5z = 14(z + 1) Combine like terms: -5 + -45 = -50 -50 + 30z + -5z = 14(z + 1) Combine like terms: 30z + -5z = 25z -50 + 25z = 14(z + 1) Reorder the terms: -50 + 25z = 14(1 + z) -50 + 25z = (1 * 14 + z * 14) -50 + 25z = (14 + 14z) Solving -50 + 25z = 14 + 14z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-14z' to each side of the equation. -50 + 25z + -14z = 14 + 14z + -14z Combine like terms: 25z + -14z = 11z -50 + 11z = 14 + 14z + -14z Combine like terms: 14z + -14z = 0 -50 + 11z = 14 + 0 -50 + 11z = 14 Add '50' to each side of the equation. -50 + 50 + 11z = 14 + 50 Combine like terms: -50 + 50 = 0 0 + 11z = 14 + 50 11z = 14 + 50 Combine like terms: 14 + 50 = 64 11z = 64 Divide each side by '11'. z = 5.818181818 Simplifying z = 5.818181818
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