Option d: [tex]-2<x<1[/tex] is the value of x.
Explanation:
The given expression is [tex]1<x+3<4[/tex]
Since, we know that, if [tex]a<u<b[/tex], then [tex]a<u[/tex] and [tex]u<b[/tex]
Thus, we have,
[tex]1<x+3[/tex]
Subtracting both sides by 3, we get,
[tex]1-3<x[/tex]
[tex]-2<x[/tex]
Also, we have,
[tex]x+3<4[/tex]
Subtracting both sides by 3, we get,
[tex]x<4-3[/tex]
[tex]x<1[/tex]
Thus, we have the intervals
[tex]-2<x[/tex] and [tex]x<1[/tex]
Combining the intervals, we get,
[tex]-2<x<1[/tex]
Thus, the value of x is [tex]-2<x<1[/tex]
