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Determine the largest integer value of [tex]\( x \)[/tex] in the solution of the following inequality.

[tex]\[ 3x + 3 \ \textless \ 12 \][/tex]

[tex]\[ x = \boxed{} \][/tex]

Sagot :

GinnyAnsweridn
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]
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