Answer :
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]
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]
