To determine which value of [tex]\( x \)[/tex] is in the solution set of the inequality [tex]\( 9(2x + 1) < 9x - 18 \)[/tex], let's solve it step-by-step.
1. Distribute the 9 on the left-hand side of the inequality:
[tex]\[
9(2x + 1) < 9x - 18
\][/tex]
Which gives:
[tex]\[
18x + 9 < 9x - 18
\][/tex]
2. Subtract [tex]\( 9x \)[/tex] from both sides of the inequality to isolate the terms involving [tex]\( x \)[/tex] on one side:
[tex]\[
18x + 9 - 9x < 9x - 18 - 9x
\][/tex]
Simplifying this, we get:
[tex]\[
9x + 9 < -18
\][/tex]
3. Subtract 9 from both sides to further isolate [tex]\( x \)[/tex]:
[tex]\[
9x + 9 - 9 < -18 - 9
\][/tex]
Simplifying this, we get:
[tex]\[
9x < -27
\][/tex]
4. Divide both sides by 9 to solve for [tex]\( x \)[/tex]:
[tex]\[
\frac{9x}{9} < \frac{-27}{9}
\][/tex]
Simplifying this, we get:
[tex]\[
x < -3
\][/tex]
Therefore, the solution to the inequality is [tex]\( x < -3 \)[/tex].
Now, we need to determine which value from the provided options [tex]\((-4, -3, -2, -1)\)[/tex] satisfies this inequality. The only value that is less than [tex]\(-3\)[/tex] is [tex]\(-4\)[/tex].
Hence, the value of [tex]\( x \)[/tex] that is in the solution set of the inequality is:
[tex]\[
\boxed{-4}
\][/tex]
