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Simplifying 5(2z + -1) + -4(z + 3) = 3(z + 1) Reorder the terms: 5(-1 + 2z) + -4(z + 3) = 3(z + 1) (-1 * 5 + 2z * 5) + -4(z + 3) = 3(z + 1) (-5 + 10z) + -4(z + 3) = 3(z + 1) Reorder the terms: -5 + 10z + -4(3 + z) = 3(z + 1) -5 + 10z + (3 * -4 + z * -4) = 3(z + 1) -5 + 10z + (-12 + -4z) = 3(z + 1) Reorder the terms: -5 + -12 + 10z + -4z = 3(z + 1) Combine like terms: -5 + -12 = -17 -17 + 10z + -4z = 3(z + 1) Combine like terms: 10z + -4z = 6z -17 + 6z = 3(z + 1) Reorder the terms: -17 + 6z = 3(1 + z) -17 + 6z = (1 * 3 + z * 3) -17 + 6z = (3 + 3z) Solving -17 + 6z = 3 + 3z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3z' to each side of the equation. -17 + 6z + -3z = 3 + 3z + -3z Combine like terms: 6z + -3z = 3z -17 + 3z = 3 + 3z + -3z Combine like terms: 3z + -3z = 0 -17 + 3z = 3 + 0 -17 + 3z = 3 Add '17' to each side of the equation. -17 + 17 + 3z = 3 + 17 Combine like terms: -17 + 17 = 0 0 + 3z = 3 + 17 3z = 3 + 17 Combine like terms: 3 + 17 = 20 3z = 20 Divide each side by '3'. z = 6.666666667 Simplifying z = 6.666666667
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