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

Sagot :

Given:

The inequalities are:

[tex]-2<x<3[/tex]

[tex]-2\leq x<2[/tex]

To find:

The integer values that satisfy both inequalities.

Solution:

We have,

[tex]-2<x<3[/tex]

[tex]-2\leq x<2[/tex]

For [tex]-2<x<3[/tex], the possible integer values are

[tex]x=-1,0,1,2[/tex]          ...(i)

For [tex]-2\leq x<2[/tex], the possible integer values are

[tex]x=-2,-1,0,1[/tex]        ...(ii)

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

[tex]x=-1,0,1[/tex]

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

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