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Simplifying 4[Z + -1(6Z + 48) + 3] = 3(Z + 9) Reorder the terms: 4[Z + -1(48 + 6Z) + 3] = 3(Z + 9) 4[Z + (48 * -1 + 6Z * -1) + 3] = 3(Z + 9) 4[Z + (-48 + -6Z) + 3] = 3(Z + 9) Reorder the terms: 4[-48 + 3 + Z + -6Z] = 3(Z + 9) Combine like terms: -48 + 3 = -45 4[-45 + Z + -6Z] = 3(Z + 9) Combine like terms: Z + -6Z = -5Z 4[-45 + -5Z] = 3(Z + 9) [-45 * 4 + -5Z * 4] = 3(Z + 9) [-180 + -20Z] = 3(Z + 9) Reorder the terms: -180 + -20Z = 3(9 + Z) -180 + -20Z = (9 * 3 + Z * 3) -180 + -20Z = (27 + 3Z) Solving -180 + -20Z = 27 + 3Z Solving for variable 'Z'. Move all terms containing Z to the left, all other terms to the right. Add '-3Z' to each side of the equation. -180 + -20Z + -3Z = 27 + 3Z + -3Z Combine like terms: -20Z + -3Z = -23Z -180 + -23Z = 27 + 3Z + -3Z Combine like terms: 3Z + -3Z = 0 -180 + -23Z = 27 + 0 -180 + -23Z = 27 Add '180' to each side of the equation. -180 + 180 + -23Z = 27 + 180 Combine like terms: -180 + 180 = 0 0 + -23Z = 27 + 180 -23Z = 27 + 180 Combine like terms: 27 + 180 = 207 -23Z = 207 Divide each side by '-23'. Z = -9 Simplifying Z = -9
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