Question

Select all the equations that have {4} as its solution set.

a. 7−x=12x

b. x² +3=10x−21

c. 5 + 2x = 3x + 3

d. 79−3x=12x+19

Answer 1

After substituting x with 4 in each equation, equations b (x² +3=10x−21) and d (79−3x=12x+19) hold true, indicating that {4} is their solution set, while equations a (7−x=12x) and c (5 + 2x = 3x + 3) do not.

Step-by-step explanation:

To find out which equations have {4} as its solution set, we need to substitute x with 4 and see if the equation holds true.

1. Equation a: 7−x=12x
   Substituting 4 for x gives us 7 − 4 = 12(4), which simplifies to 3 = 48. This is not true, so this equation does not have {4} as its solution set.
2. Equation b: x² +3=10x−21
   Substituting 4 for x gives us 4² + 3 = 10(4) − 21, which simplifies to 16 + 3 = 40 − 21, or 19 = 19. This is true, so equation b has {4} as its solution.
3. Equation c: 5 + 2x = 3x + 3
   Substituting 4 for x gives us 5 + 2(4) = 3(4) + 3, which simplifies to 5 + 8 = 12 + 3, or 13 = 15. This is not true, so equation c does not have {4} as its solution.
4. Equation d: 79−3x=12x+19
   Substituting 4 for x gives us 79 − 3(4) = 12(4) + 19, which simplifies to 79 − 12 = 48 + 19, or 67 = 67. This is true, so equation d has {4} as its solution.

After testing all the equations, we find that equations b and d have {4} as their solution set.