To find the largest integer value that [tex]\( x \)[/tex] could take such that [tex]\( x + 8 < 12 \)[/tex] is still true, follow these steps:
1. Start with the inequality:
[tex]\[
x + 8 < 12
\][/tex]
2. Isolate [tex]\( x \)[/tex] on one side of the inequality: To do this, subtract 8 from both sides of the inequality:
[tex]\[
x + 8 - 8 < 12 - 8
\][/tex]
3. Simplify the inequality:
[tex]\[
x < 4
\][/tex]
Now, we need to determine the largest integer that satisfies this inequality [tex]\( x < 4 \)[/tex].
4. Consider the integers less than 4:
- [tex]\( 3 \)[/tex]
- [tex]\( 2 \)[/tex]
- [tex]\( 1 \)[/tex]
- and so on
5. Identify the largest integer in this list: The largest integer that is less than 4 is:
[tex]\[
3
\][/tex]
Therefore, the solution is:
[tex]\[
\boxed{3}
\][/tex]
