To solve for [tex]\( d \)[/tex] given the inequalities:
[tex]\[
4 - d < 4 + d
\][/tex]
[tex]\( d > 0 \)[/tex]
[tex]\( d > -4 \)[/tex]
[tex]\( d > 8 \)[/tex]
[tex]\( d > -8 \)[/tex]
Let's break this down step by step:
1. Solve the inequality [tex]\( 4 - d < 4 + d \)[/tex]:
[tex]\[
4 - d < 4 + d
\][/tex]
Subtract [tex]\( 4 \)[/tex] from both sides:
[tex]\[
-d < d
\][/tex]
Add [tex]\( d \)[/tex] to both sides:
[tex]\[
0 < 2d
\][/tex]
Divide both sides by [tex]\( 2 \)[/tex]:
[tex]\[
0 < d
\][/tex]
This simplifies to:
[tex]\[
d > 0
\][/tex]
2. Consider the inequalities:
- [tex]\( d > 0 \)[/tex]
- [tex]\( d > -4 \)[/tex]
- [tex]\( d > 8 \)[/tex]
- [tex]\( d > -8 \)[/tex]
The strictest constraint among these is [tex]\( d > 8 \)[/tex]. Even though [tex]\( d \)[/tex] being greater than all the negative values and zero is true, the most limiting condition here is [tex]\( d > 8 \)[/tex].
Thus, the solution to the given inequalities, considering the strictest condition, is:
[tex]\[
d = 8
\][/tex]
