To determine the largest integer value of [tex]\( x \)[/tex] in the inequality [tex]\( 3x + 3 < 12 \)[/tex], follow these steps:
1. Start by isolating [tex]\( x \)[/tex] in the inequality:
[tex]\[
3x + 3 < 12
\][/tex]
2. Subtract 3 from both sides of the inequality to move the constant term:
[tex]\[
3x < 12 - 3
\][/tex]
Simplifying the right-hand side:
[tex]\[
3x < 9
\][/tex]
3. Next, divide both sides by 3 to solve for [tex]\( x \)[/tex]:
[tex]\[
x < \frac{9}{3}
\][/tex]
Simplifying the fraction:
[tex]\[
x < 3
\][/tex]
4. Identify the largest integer value less than 3:
Since [tex]\( x \)[/tex] must be less than 3, the largest integer that satisfies this inequality is 2.
Hence, the largest integer value of [tex]\( x \)[/tex] that satisfies the inequality [tex]\( 3x + 3 < 12 \)[/tex] is:
[tex]\[
\boxed{2}
\][/tex]
