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Simplifying 3(4Z + -1) + -4(Z + 5) = 4(Z + 1) Reorder the terms: 3(-1 + 4Z) + -4(Z + 5) = 4(Z + 1) (-1 * 3 + 4Z * 3) + -4(Z + 5) = 4(Z + 1) (-3 + 12Z) + -4(Z + 5) = 4(Z + 1) Reorder the terms: -3 + 12Z + -4(5 + Z) = 4(Z + 1) -3 + 12Z + (5 * -4 + Z * -4) = 4(Z + 1) -3 + 12Z + (-20 + -4Z) = 4(Z + 1) Reorder the terms: -3 + -20 + 12Z + -4Z = 4(Z + 1) Combine like terms: -3 + -20 = -23 -23 + 12Z + -4Z = 4(Z + 1) Combine like terms: 12Z + -4Z = 8Z -23 + 8Z = 4(Z + 1) Reorder the terms: -23 + 8Z = 4(1 + Z) -23 + 8Z = (1 * 4 + Z * 4) -23 + 8Z = (4 + 4Z) Solving -23 + 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. -23 + 8Z + -4Z = 4 + 4Z + -4Z Combine like terms: 8Z + -4Z = 4Z -23 + 4Z = 4 + 4Z + -4Z Combine like terms: 4Z + -4Z = 0 -23 + 4Z = 4 + 0 -23 + 4Z = 4 Add '23' to each side of the equation. -23 + 23 + 4Z = 4 + 23 Combine like terms: -23 + 23 = 0 0 + 4Z = 4 + 23 4Z = 4 + 23 Combine like terms: 4 + 23 = 27 4Z = 27 Divide each side by '4'. Z = 6.75 Simplifying Z = 6.75
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