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Simplifying 6(5z + -1) + -5(z + 6) = 14(z + 1) Reorder the terms: 6(-1 + 5z) + -5(z + 6) = 14(z + 1) (-1 * 6 + 5z * 6) + -5(z + 6) = 14(z + 1) (-6 + 30z) + -5(z + 6) = 14(z + 1) Reorder the terms: -6 + 30z + -5(6 + z) = 14(z + 1) -6 + 30z + (6 * -5 + z * -5) = 14(z + 1) -6 + 30z + (-30 + -5z) = 14(z + 1) Reorder the terms: -6 + -30 + 30z + -5z = 14(z + 1) Combine like terms: -6 + -30 = -36 -36 + 30z + -5z = 14(z + 1) Combine like terms: 30z + -5z = 25z -36 + 25z = 14(z + 1) Reorder the terms: -36 + 25z = 14(1 + z) -36 + 25z = (1 * 14 + z * 14) -36 + 25z = (14 + 14z) Solving -36 + 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. -36 + 25z + -14z = 14 + 14z + -14z Combine like terms: 25z + -14z = 11z -36 + 11z = 14 + 14z + -14z Combine like terms: 14z + -14z = 0 -36 + 11z = 14 + 0 -36 + 11z = 14 Add '36' to each side of the equation. -36 + 36 + 11z = 14 + 36 Combine like terms: -36 + 36 = 0 0 + 11z = 14 + 36 11z = 14 + 36 Combine like terms: 14 + 36 = 50 11z = 50 Divide each side by '11'. z = 4.545454545 Simplifying z = 4.545454545
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