Question

Which statement is correct?

A. The equation 3(3x-2)-4=5x has no solution
B. The equation 4(2x-3)-5=4x has exactly one solution
C. The equation 5(3x-2)-2=3x has exactly two solutions
D. The equation 6(2x-3)-3=2x has infinitely many solutions

Answer 1

We can conclude that only option B is correct.

Explanation:

A. The equation 3(3x - 2) - 4 = 5x has a solution.

Solving it we get,

3(3x - 2) - 4 = 5x

⇒ 9x - 6 - 4 = 5x

⇒ 4x = 10

⇒ x = 2.5

B. The equation 4(2x - 3) - 5 = 4x has exactly one solution.

Solving it we get,

4(2x - 3) - 5 = 4x

⇒ 8x - 12 - 5 = 4x

⇒ 4x = 17

⇒ x = 4.25

C. The equation 5(3x - 2) - 2 = 3x also has exactly one solution.

Solving it we get,

5(3x - 2) - 2 = 3x

⇒ 15x - 10 - 2 = 3x

⇒ 12x = 12

⇒ x = 1

D. The equation 6(2x - 3) - 3 = 2x also has exactly one solution.

Solving it we get,

6(2x - 3) - 3 = 2x

⇒ 12x - 18 - 3 = 2x

⇒ 10x = 21

⇒ x = 2.1

Therefore, we can conclude that only option B is correct. (Answer)