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Simplifying 5(2z + -1) + -4(z + 3) = 2(z + 1) Reorder the terms: 5(-1 + 2z) + -4(z + 3) = 2(z + 1) (-1 * 5 + 2z * 5) + -4(z + 3) = 2(z + 1) (-5 + 10z) + -4(z + 3) = 2(z + 1) Reorder the terms: -5 + 10z + -4(3 + z) = 2(z + 1) -5 + 10z + (3 * -4 + z * -4) = 2(z + 1) -5 + 10z + (-12 + -4z) = 2(z + 1) Reorder the terms: -5 + -12 + 10z + -4z = 2(z + 1) Combine like terms: -5 + -12 = -17 -17 + 10z + -4z = 2(z + 1) Combine like terms: 10z + -4z = 6z -17 + 6z = 2(z + 1) Reorder the terms: -17 + 6z = 2(1 + z) -17 + 6z = (1 * 2 + z * 2) -17 + 6z = (2 + 2z) Solving -17 + 6z = 2 + 2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2z' to each side of the equation. -17 + 6z + -2z = 2 + 2z + -2z Combine like terms: 6z + -2z = 4z -17 + 4z = 2 + 2z + -2z Combine like terms: 2z + -2z = 0 -17 + 4z = 2 + 0 -17 + 4z = 2 Add '17' to each side of the equation. -17 + 17 + 4z = 2 + 17 Combine like terms: -17 + 17 = 0 0 + 4z = 2 + 17 4z = 2 + 17 Combine like terms: 2 + 17 = 19 4z = 19 Divide each side by '4'. z = 4.75 Simplifying z = 4.75
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