Consider the equation 2(ax+3)=4x−3(4x+8). For what value of a is there no solution to the equation?

Considering the equation  

The equation given above has no solution when  a = -4

On  simplifying the given equation we can find that

The equation  has no solution when the equality of both sides does not hold true .

Hence by observation we can say that the equation has no solution when

So the equation given above has no solution when  a = -4.

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the value of such that  there is no solution to the equation is .

Step-by-step explanation:

Let first simplify the expression presented on statement. The equation has no solution if and only if is eliminated in the process and an absurd is the result (i.e. ).

To obtain an absurd, we need that . Hence, the value of such that  there is no solution to the equation is:

Let prove the certainty of the result. We find that an absurd exist: ()