To solve the inequality [tex]\( 5x < 16 + x \)[/tex], follow these steps:
1. Isolate the variable on one side of the inequality:
Begin by subtracting [tex]\( x \)[/tex] from both sides of the inequality to simplify:
[tex]\[
5x - x < 16
\][/tex]
2. Combine like terms:
[tex]\[
4x < 16
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
Next, divide both sides of the inequality by 4 to isolate [tex]\( x \)[/tex]:
[tex]\[
\frac{4x}{4} < \frac{16}{4}
\][/tex]
Simplifying the fractions, we get:
[tex]\[
x < 4
\][/tex]
4. Interpret the solution:
So, the solution to the inequality [tex]\( 5x < 16 + x \)[/tex] is [tex]\( x < 4 \)[/tex].
The correct choice from the given options is:
[tex]\[
\boxed{x < 4}
\][/tex]
