State restrictions first. Find the LCD, clear all denominators, solve, and check every proposed solution in...

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State restrictions first. Find the LCD, clear all denominators, solve, and check every proposed solution in the original equation.
1. z/5 = 4
2. 12/z = 3
3. (z + 4)/3 = 7
4. 2z/(z + 1) = 3
5. 1/z - 1/z = 3
6. 3/(z - 1) = 2/(z + 1)

SnapAndSolve AI · Accepted Answer

Restrictions: None. Solution: Multiply both sides by 5: z = 20. Restrictions: z ≠ 0. Solution: Multiply both sides by z: 12 = 3z, so z = 4. Restrictions: None. Solution: Multiply both sides by 3: z + 4 = 21, so z = 17. Restrictions: z ≠ -1. Solution: Multiply both sides by (z + 1): 2z = 3(z + 1), so 2z = 3z + 3, z = -3. Restrictions: z ≠ 0. Solution: This equation simplifies to 0 = 3, which is a contradiction. No solution. Restrictions: z ≠ 1, z ≠ -1. Solution: Multiply both sides by (z - 1)(z + 1): 3(z + 1) = 2(z - 1), so 3z + 3 = 2z - 2, z = -5.

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State restrictions first. Find the LCD, clear all denominators, solve, and check every proposed solution in...

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