To determine which values of [tex]\( x \)[/tex] satisfy the inequality [tex]\( 2x < 9 \)[/tex], we will evaluate the inequality for each given value of [tex]\( x \)[/tex].
1. For [tex]\( x = 5.5 \)[/tex]:
[tex]\[
2 \cdot 5.5 = 11
\][/tex]
Since [tex]\( 11 \)[/tex] is not less than [tex]\( 9 \)[/tex], [tex]\( x = 5.5 \)[/tex] does not satisfy the inequality [tex]\( 2x < 9 \)[/tex].
2. For [tex]\( x = 4.5 \)[/tex]:
[tex]\[
2 \cdot 4.5 = 9
\][/tex]
Since [tex]\( 9 \)[/tex] is not less than [tex]\( 9 \)[/tex], [tex]\( x = 4.5 \)[/tex] does not satisfy the inequality [tex]\( 2x < 9 \)[/tex].
3. For [tex]\( x = 6 \)[/tex]:
[tex]\[
2 \cdot 6 = 12
\][/tex]
Since [tex]\( 12 \)[/tex] is not less than [tex]\( 9 \)[/tex], [tex]\( x = 6 \)[/tex] does not satisfy the inequality [tex]\( 2x < 9 \)[/tex].
4. For [tex]\( x = 4 \)[/tex]:
[tex]\[
2 \cdot 4 = 8
\][/tex]
Since [tex]\( 8 \)[/tex] is less than [tex]\( 9 \)[/tex], [tex]\( x = 4 \)[/tex] does satisfy the inequality [tex]\( 2x < 9 \)[/tex].
Therefore, among the given values, the only value that is a solution to the inequality [tex]\( 2x < 9 \)[/tex] is [tex]\( x = 4 \)[/tex].
