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Simplifying 5(2z + -1) + -2(z + 4) = 4(z + 1) Reorder the terms: 5(-1 + 2z) + -2(z + 4) = 4(z + 1) (-1 * 5 + 2z * 5) + -2(z + 4) = 4(z + 1) (-5 + 10z) + -2(z + 4) = 4(z + 1) Reorder the terms: -5 + 10z + -2(4 + z) = 4(z + 1) -5 + 10z + (4 * -2 + z * -2) = 4(z + 1) -5 + 10z + (-8 + -2z) = 4(z + 1) Reorder the terms: -5 + -8 + 10z + -2z = 4(z + 1) Combine like terms: -5 + -8 = -13 -13 + 10z + -2z = 4(z + 1) Combine like terms: 10z + -2z = 8z -13 + 8z = 4(z + 1) Reorder the terms: -13 + 8z = 4(1 + z) -13 + 8z = (1 * 4 + z * 4) -13 + 8z = (4 + 4z) Solving -13 + 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. -13 + 8z + -4z = 4 + 4z + -4z Combine like terms: 8z + -4z = 4z -13 + 4z = 4 + 4z + -4z Combine like terms: 4z + -4z = 0 -13 + 4z = 4 + 0 -13 + 4z = 4 Add '13' to each side of the equation. -13 + 13 + 4z = 4 + 13 Combine like terms: -13 + 13 = 0 0 + 4z = 4 + 13 4z = 4 + 13 Combine like terms: 4 + 13 = 17 4z = 17 Divide each side by '4'. z = 4.25 Simplifying z = 4.25
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