Question

The product of 7 and a number, x, increased by 1 is between 15 and 43. What is the compound inequality that represents the situation?

Answer 1

Let's assume that number as x

The product of 7 and a number =7x

and then increased by 1

so, it will become

=7x+1

now, it is between 15 and 43

so, we can write as

`15<7x+1<43`

now, we can solve for x

Since, we have to isolate x

step-1:

Subtract all the sides by 1

`15-1<7x+1-1<43-1`

`14<7x<42`

step-2:

Divide all the sides by 7

`(14)/(7)<(7x)/(7)<(42)/(7)`

`2<x<6`

so, solution is

`2<x<6`.............Answer