Answer:
[tex]2 < y < 12[/tex]
Step-by-step explanation:
Given
[tex]x = 7[/tex]
[tex]z = 5[/tex]
Required
What must be true about y?
To answer this, we first calculate the range as follows;
[tex]Minimum = |x - z|[/tex]
and
[tex]Maximum = |x + z|[/tex]
For Minimum, we have:
[tex]Minimum = |7 - 5|[/tex]
[tex]Minimum = |2|[/tex]
[tex]Minimum = 2[/tex]
For Maximum, we have:
[tex]Maximum = |7 + 5|[/tex]
[tex]Maximum = |12|[/tex]
[tex]Maximum = 12[/tex]
The values of y are then bounded by the following:
[tex]Minimum < y < Maximum[/tex]
This gives
[tex]2 < y < 12[/tex]
