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Simplifying 13(Z + 2) + -4(Z + -3) = 4(Z + -1) + 4(Z + -2) Reorder the terms: 13(2 + Z) + -4(Z + -3) = 4(Z + -1) + 4(Z + -2) (2 * 13 + Z * 13) + -4(Z + -3) = 4(Z + -1) + 4(Z + -2) (26 + 13Z) + -4(Z + -3) = 4(Z + -1) + 4(Z + -2) Reorder the terms: 26 + 13Z + -4(-3 + Z) = 4(Z + -1) + 4(Z + -2) 26 + 13Z + (-3 * -4 + Z * -4) = 4(Z + -1) + 4(Z + -2) 26 + 13Z + (12 + -4Z) = 4(Z + -1) + 4(Z + -2) Reorder the terms: 26 + 12 + 13Z + -4Z = 4(Z + -1) + 4(Z + -2) Combine like terms: 26 + 12 = 38 38 + 13Z + -4Z = 4(Z + -1) + 4(Z + -2) Combine like terms: 13Z + -4Z = 9Z 38 + 9Z = 4(Z + -1) + 4(Z + -2) Reorder the terms: 38 + 9Z = 4(-1 + Z) + 4(Z + -2) 38 + 9Z = (-1 * 4 + Z * 4) + 4(Z + -2) 38 + 9Z = (-4 + 4Z) + 4(Z + -2) Reorder the terms: 38 + 9Z = -4 + 4Z + 4(-2 + Z) 38 + 9Z = -4 + 4Z + (-2 * 4 + Z * 4) 38 + 9Z = -4 + 4Z + (-8 + 4Z) Reorder the terms: 38 + 9Z = -4 + -8 + 4Z + 4Z Combine like terms: -4 + -8 = -12 38 + 9Z = -12 + 4Z + 4Z Combine like terms: 4Z + 4Z = 8Z 38 + 9Z = -12 + 8Z Solving 38 + 9Z = -12 + 8Z Solving for variable 'Z'. Move all terms containing Z to the left, all other terms to the right. Add '-8Z' to each side of the equation. 38 + 9Z + -8Z = -12 + 8Z + -8Z Combine like terms: 9Z + -8Z = 1Z 38 + 1Z = -12 + 8Z + -8Z Combine like terms: 8Z + -8Z = 0 38 + 1Z = -12 + 0 38 + 1Z = -12 Add '-38' to each side of the equation. 38 + -38 + 1Z = -12 + -38 Combine like terms: 38 + -38 = 0 0 + 1Z = -12 + -38 1Z = -12 + -38 Combine like terms: -12 + -38 = -50 1Z = -50 Divide each side by '1'. Z = -50 Simplifying Z = -50
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