High School

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------------------------------------------------ Work out the largest integer value that [tex]$x$[/tex] could take if:

[tex]\[ x + 8 \ < \ 12 \][/tex]

Answer :

We start with the inequality
[tex]$$
x + 8 < 12.
$$[/tex]

Step 1: Isolate [tex]\( x \)[/tex].

Subtract [tex]\( 8 \)[/tex] from both sides:
[tex]$$
x + 8 - 8 < 12 - 8.
$$[/tex]

This simplifies to:
[tex]$$
x < 4.
$$[/tex]

Step 2: Determine the largest integer satisfying the inequality.

Since [tex]\( x \)[/tex] must be strictly less than [tex]\( 4 \)[/tex], the possible values of [tex]\( x \)[/tex] include all numbers less than [tex]\( 4 \)[/tex]. The largest integer less than [tex]\( 4 \)[/tex] is:
[tex]$$
3.
$$[/tex]

Thus, the largest integer that [tex]\( x \)[/tex] can take is [tex]\( \boxed{3} \)[/tex].

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