Question

For the equation 21+3x=3x+k, which value of K will create a false equation with no solution

A) 3x
B) 15
C) 21

Answer 1

OPTION B: K = 15

Explanation:

The given equation is: 21 + 3x = 3x + K

Substitute K = 3x

we get: 21 = 3x + 3x + 3x

⇒ 21 + 3x = 6x

⇒ 21 = 3x

This gives the value of x = 7. That means K = 3x gives us a solution. So, OPTION A is eliminated.

Now, K = 15

The equation becomes 21 + 3x = 3x + 15

Subtracting 3x on both the sides, we get:

⇒ 21 + 3x - 3x = 15 + 3x - 3x

⇒ 21 = 15 which can not be correct. So, K = 15 renders the equation meaningless and hence with no solution.

So, OPTION B is the answer.

Note that K = 21 will give the equation with infinitely many solutions.