Question

What integer values satisfy both inequalities? − 2 < x < 3 − 2 ≤ x < 2

Answer 1

Given:

The inequalities are:

`-2<x<3`

`-2\leq x<2`

To find:

The integer values that satisfy both inequalities.

Solution:

We have,

`-2<x<3`

`-2\leq x<2`

For
`-2<x<3`, the possible integer values are

`x=-1,0,1,2` ...(i)

For
`-2\leq x<2`, the possible integer values are

`x=-2,-1,0,1` ...(ii)

The common values of x in (i) and (ii) are

`x=-1,0,1`

Therefore, the integer values -1, 0 and 1 satisfy both inequalities.