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Simplifying 6(5z + -1) + -5(z + 6) = 19(z + 1) Reorder the terms: 6(-1 + 5z) + -5(z + 6) = 19(z + 1) (-1 * 6 + 5z * 6) + -5(z + 6) = 19(z + 1) (-6 + 30z) + -5(z + 6) = 19(z + 1) Reorder the terms: -6 + 30z + -5(6 + z) = 19(z + 1) -6 + 30z + (6 * -5 + z * -5) = 19(z + 1) -6 + 30z + (-30 + -5z) = 19(z + 1) Reorder the terms: -6 + -30 + 30z + -5z = 19(z + 1) Combine like terms: -6 + -30 = -36 -36 + 30z + -5z = 19(z + 1) Combine like terms: 30z + -5z = 25z -36 + 25z = 19(z + 1) Reorder the terms: -36 + 25z = 19(1 + z) -36 + 25z = (1 * 19 + z * 19) -36 + 25z = (19 + 19z) Solving -36 + 25z = 19 + 19z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-19z' to each side of the equation. -36 + 25z + -19z = 19 + 19z + -19z Combine like terms: 25z + -19z = 6z -36 + 6z = 19 + 19z + -19z Combine like terms: 19z + -19z = 0 -36 + 6z = 19 + 0 -36 + 6z = 19 Add '36' to each side of the equation. -36 + 36 + 6z = 19 + 36 Combine like terms: -36 + 36 = 0 0 + 6z = 19 + 36 6z = 19 + 36 Combine like terms: 19 + 36 = 55 6z = 55 Divide each side by '6'. z = 9.166666667 Simplifying z = 9.166666667
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