Question

The solution of the inequality $ax-2<-4$ is $x<-1$ . Find the value of a.

Short answer

The value of a is $a>2$.

Step-by-step solution

Step 1.  Apply the concept of Linear inequalities

In this type of question, apply the concept of basic linear inequalities to get the equivalent by multiplying the number or dividing the numbers and also using the reverse inequality concept.

Step 2.  Finding whether it is equivalent or not

Since, the expression is $ax-2<-4$.

Now, simply adding $-2$to both side of the inequality and also use the reverse inequality concept and also put

$\begin{array}{l}ax-2<-4\\ ax-2+2<-4+2\\ ax<-2\\ a(-1)<-2(x<-1)\\ \frac{-a}{-1}<\frac{-2}{-1}\\ a>2\end{array}$