Question

For which value of c will the equation 6x+c=2(3x+1) have no solution? Select all that apply.

Question 2 options:

1


2


3


4

Answer 1

1, 3, 4

Explanation:

6x + c = 2(3x + 1) use the distributive property a(b + c) = ab + ac

6x + c = (2)(3x) + (2)(1)

6x + c = 6x + 2 subtract 6x from both sides

6x - 6x + c = 6x - 6x + 2

c = 2

The equation has no solution if we get a false equation without the variable y.

Therefore c ≠ 2.

Answer 2

1, 3, 4

Explanation:

Given equation,

6x + c = 2(3x + 1),

⇒ 6x + c = 6x + 2 ( By distributive property ),

⇒ c = 2 -----(1) ,

∵ An equation has no solution when after solving the equation we get a false statement,

if c = 1,

From equation (1),

1 = 2 ( False )

⇒ given equation has no solution,

if c = 2,

From equation (1),

2 = 2 ( True )

⇒ the given equation has infinitely many solutions,

if c = 3,

From equation (1),

3 = 2 ( False )

⇒ the given equation has no solution,

if c = 4,

From equation (1),

4 = 2 ( False )

⇒ the given equation has no solutions.