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Simplifying 5(6z + -1) + -2(z + 8) = 17(z + 1) Reorder the terms: 5(-1 + 6z) + -2(z + 8) = 17(z + 1) (-1 * 5 + 6z * 5) + -2(z + 8) = 17(z + 1) (-5 + 30z) + -2(z + 8) = 17(z + 1) Reorder the terms: -5 + 30z + -2(8 + z) = 17(z + 1) -5 + 30z + (8 * -2 + z * -2) = 17(z + 1) -5 + 30z + (-16 + -2z) = 17(z + 1) Reorder the terms: -5 + -16 + 30z + -2z = 17(z + 1) Combine like terms: -5 + -16 = -21 -21 + 30z + -2z = 17(z + 1) Combine like terms: 30z + -2z = 28z -21 + 28z = 17(z + 1) Reorder the terms: -21 + 28z = 17(1 + z) -21 + 28z = (1 * 17 + z * 17) -21 + 28z = (17 + 17z) Solving -21 + 28z = 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. -21 + 28z + -17z = 17 + 17z + -17z Combine like terms: 28z + -17z = 11z -21 + 11z = 17 + 17z + -17z Combine like terms: 17z + -17z = 0 -21 + 11z = 17 + 0 -21 + 11z = 17 Add '21' to each side of the equation. -21 + 21 + 11z = 17 + 21 Combine like terms: -21 + 21 = 0 0 + 11z = 17 + 21 11z = 17 + 21 Combine like terms: 17 + 21 = 38 11z = 38 Divide each side by '11'. z = 3.454545455 Simplifying z = 3.454545455
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