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Simplifying 5(4z + -1) + -3(z + 4) = 6(z + 1) Reorder the terms: 5(-1 + 4z) + -3(z + 4) = 6(z + 1) (-1 * 5 + 4z * 5) + -3(z + 4) = 6(z + 1) (-5 + 20z) + -3(z + 4) = 6(z + 1) Reorder the terms: -5 + 20z + -3(4 + z) = 6(z + 1) -5 + 20z + (4 * -3 + z * -3) = 6(z + 1) -5 + 20z + (-12 + -3z) = 6(z + 1) Reorder the terms: -5 + -12 + 20z + -3z = 6(z + 1) Combine like terms: -5 + -12 = -17 -17 + 20z + -3z = 6(z + 1) Combine like terms: 20z + -3z = 17z -17 + 17z = 6(z + 1) Reorder the terms: -17 + 17z = 6(1 + z) -17 + 17z = (1 * 6 + z * 6) -17 + 17z = (6 + 6z) Solving -17 + 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. -17 + 17z + -6z = 6 + 6z + -6z Combine like terms: 17z + -6z = 11z -17 + 11z = 6 + 6z + -6z Combine like terms: 6z + -6z = 0 -17 + 11z = 6 + 0 -17 + 11z = 6 Add '17' to each side of the equation. -17 + 17 + 11z = 6 + 17 Combine like terms: -17 + 17 = 0 0 + 11z = 6 + 17 11z = 6 + 17 Combine like terms: 6 + 17 = 23 11z = 23 Divide each side by '11'. z = 2.090909091 Simplifying z = 2.090909091
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