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Simplifying 5(2z + -1) + -2(z + 3) = 4(z + 1) Reorder the terms: 5(-1 + 2z) + -2(z + 3) = 4(z + 1) (-1 * 5 + 2z * 5) + -2(z + 3) = 4(z + 1) (-5 + 10z) + -2(z + 3) = 4(z + 1) Reorder the terms: -5 + 10z + -2(3 + z) = 4(z + 1) -5 + 10z + (3 * -2 + z * -2) = 4(z + 1) -5 + 10z + (-6 + -2z) = 4(z + 1) Reorder the terms: -5 + -6 + 10z + -2z = 4(z + 1) Combine like terms: -5 + -6 = -11 -11 + 10z + -2z = 4(z + 1) Combine like terms: 10z + -2z = 8z -11 + 8z = 4(z + 1) Reorder the terms: -11 + 8z = 4(1 + z) -11 + 8z = (1 * 4 + z * 4) -11 + 8z = (4 + 4z) Solving -11 + 8z = 4 + 4z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4z' to each side of the equation. -11 + 8z + -4z = 4 + 4z + -4z Combine like terms: 8z + -4z = 4z -11 + 4z = 4 + 4z + -4z Combine like terms: 4z + -4z = 0 -11 + 4z = 4 + 0 -11 + 4z = 4 Add '11' to each side of the equation. -11 + 11 + 4z = 4 + 11 Combine like terms: -11 + 11 = 0 0 + 4z = 4 + 11 4z = 4 + 11 Combine like terms: 4 + 11 = 15 4z = 15 Divide each side by '4'. z = 3.75 Simplifying z = 3.75
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