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Simplifying 6(5z + -1) + -5(z + 2) = 17(z + 1) Reorder the terms: 6(-1 + 5z) + -5(z + 2) = 17(z + 1) (-1 * 6 + 5z * 6) + -5(z + 2) = 17(z + 1) (-6 + 30z) + -5(z + 2) = 17(z + 1) Reorder the terms: -6 + 30z + -5(2 + z) = 17(z + 1) -6 + 30z + (2 * -5 + z * -5) = 17(z + 1) -6 + 30z + (-10 + -5z) = 17(z + 1) Reorder the terms: -6 + -10 + 30z + -5z = 17(z + 1) Combine like terms: -6 + -10 = -16 -16 + 30z + -5z = 17(z + 1) Combine like terms: 30z + -5z = 25z -16 + 25z = 17(z + 1) Reorder the terms: -16 + 25z = 17(1 + z) -16 + 25z = (1 * 17 + z * 17) -16 + 25z = (17 + 17z) Solving -16 + 25z = 17 + 17z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-17z' to each side of the equation. -16 + 25z + -17z = 17 + 17z + -17z Combine like terms: 25z + -17z = 8z -16 + 8z = 17 + 17z + -17z Combine like terms: 17z + -17z = 0 -16 + 8z = 17 + 0 -16 + 8z = 17 Add '16' to each side of the equation. -16 + 16 + 8z = 17 + 16 Combine like terms: -16 + 16 = 0 0 + 8z = 17 + 16 8z = 17 + 16 Combine like terms: 17 + 16 = 33 8z = 33 Divide each side by '8'. z = 4.125 Simplifying z = 4.125
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