What value of d will make the equation have no solutions?

Question

5(4-8x)=d(5-6x)-4x

 

What value of d will make the equation have no solutions?

Answer 1

Keep in mind that ax+b = ax+c has no solution if b≠c,

because if you subtract ax from both sides you get

b=c which is a contradiction.

 

5(4-8x) = 20-40x = d(5-6x)-4x = 5d-(6d)x-4x =5d-(6d+4)x

Set 40 = 6d+4 and solve for d:

d=6.

 

Now check if d=6 works.

If d=6, the above equation becomes:

5(4-8x) = 20-40x = 6(5-6x)-4x = 30-36x-4x = 30-40x.

So,  there is no solution.

Answer 2

5(4 - 8x) = d(5 - 6x) - 4x

20 - 40x = d(5 - 6x) - 4x

20 - 36x = d(5 - 6x)

 

All values of d make the equation have not solution.