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Simplifying 5(4z + -1) + -3(z + 9) = 6(z + 1) Reorder the terms: 5(-1 + 4z) + -3(z + 9) = 6(z + 1) (-1 * 5 + 4z * 5) + -3(z + 9) = 6(z + 1) (-5 + 20z) + -3(z + 9) = 6(z + 1) Reorder the terms: -5 + 20z + -3(9 + z) = 6(z + 1) -5 + 20z + (9 * -3 + z * -3) = 6(z + 1) -5 + 20z + (-27 + -3z) = 6(z + 1) Reorder the terms: -5 + -27 + 20z + -3z = 6(z + 1) Combine like terms: -5 + -27 = -32 -32 + 20z + -3z = 6(z + 1) Combine like terms: 20z + -3z = 17z -32 + 17z = 6(z + 1) Reorder the terms: -32 + 17z = 6(1 + z) -32 + 17z = (1 * 6 + z * 6) -32 + 17z = (6 + 6z) Solving -32 + 17z = 6 + 6z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-6z' to each side of the equation. -32 + 17z + -6z = 6 + 6z + -6z Combine like terms: 17z + -6z = 11z -32 + 11z = 6 + 6z + -6z Combine like terms: 6z + -6z = 0 -32 + 11z = 6 + 0 -32 + 11z = 6 Add '32' to each side of the equation. -32 + 32 + 11z = 6 + 32 Combine like terms: -32 + 32 = 0 0 + 11z = 6 + 32 11z = 6 + 32 Combine like terms: 6 + 32 = 38 11z = 38 Divide each side by '11'. z = 3.454545455 Simplifying z = 3.454545455
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