Question

What value of b will cause the equation below to have no solution for x(4b+2)x-7=10bx-12

Answer 1

The value of b for the equation to have no solution is;

`b=(1)/(3)`

Step-by-step explanation:

Given the the equation;

`(4b+2)x-7=10bx-12`

solving we have;

`\begin{gathered} 4bx+2x-7=10bx-12 \\ 2x+4bx-10bx=-12+7 \\ 2x-6bx=-5 \\ x(2-6b)=-5 \end{gathered}`

for x to have a solution, the product of x and (2-6b) must not be equal to zero.

So, the value of b for the equation to have no solution can be derived by equating (2-6b) to zero;

`\begin{gathered} (2-6b)=0 \\ 2=6b\text{ -----add 6b to both sides} \\ b=(2)/(6)\text{ ------divide both sides by 6} \\ b=(1)/(3) \end{gathered}`

Therefore, the value of b for the equation to have no solution is;

`b=(1)/(3)`