Question

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

Answer 1

Answer:

the value of $a$ such that  there is no solution to the equation is $a = -4$.

Step-by-step explanation:

Let first simplify the expression presented on statement. The equation has no solution if and only if $a$ is eliminated in the process and an absurd is the result (i.e. $0 = 7$).

$2\cdot (a\cdot x + 3) = 4\cdot x -3\cdot (4\cdot x + 8)$

$2\cdot a\cdot x +6 = 4\cdot x -12\cdot x -24$

$2\cdot a \cdot x+6=-8\cdot x-24$

$2\cdot a\cdot x +8\cdot x = -30$

$2\cdot (a+4)\cdot x = -30$

$(a+4)\cdot x = -15$

To obtain an absurd, we need that $a+4 = 0$. Hence, the value of $a$ such that  there is no solution to the equation is:

$a = -4$

Let prove the certainty of the result. We find that an absurd exist: ($a = -4$)

$0 = -15$