To determine if [tex]\(0\)[/tex] is a solution to the inequality [tex]\(-4 < w + 4 \leq 6\)[/tex], let's break it down step-by-step:
1. Substitute [tex]\(w\)[/tex] with 0:
[tex]\[
-4 < 0 + 4 \leq 6
\][/tex]
2. Simplify the expression inside the inequality:
[tex]\[
-4 < 4 \leq 6
\][/tex]
3. Check the left side of the inequality:
[tex]\[
-4 < 4
\][/tex]
This statement is true because [tex]\(-4\)[/tex] is indeed less than [tex]\(4\)[/tex].
4. Check the right side of the inequality:
[tex]\[
4 \leq 6
\][/tex]
This statement is also true because [tex]\(4\)[/tex] is less than or equal to [tex]\(6\)[/tex].
Since both parts of the inequality are satisfied, the number 0 is indeed a solution. Therefore, the answer is:
True
