## Algebra 1

The other inequalities with $a$ as a solution are those with a smaller denominator.
The pattern of inequalities $\frac{x}{2} \lt 10$, $\frac{x}{3} \lt 10$, $\frac{x}{4} \lt 10$, etc., has the pattern of solutions $x < 10$, $x < 20$, $x < 30$ (and so on). As an example, if $a = 40$, the applicable inequality this value of $a$ would be an answer for is $\frac{x}{4} \lt 10$. However, this answer would also be valid for the inequalities $\frac{x}{2} \lt 10$, $\frac{x}{3} \lt 10$, $\frac{x}{4} \lt 10$.