Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 3 - Solving Inequalities - 3-3 Solving Inequalities Using Multiplication or Division - Practice and Problem-Solving Exercises: 61

Answer

The other inequalities with $a$ as a solution are those with a smaller denominator.

Work Step by Step

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 $\frac{x}{2} \lt 10$, $\frac{x}{3} \lt 10$, $\frac{x}{4} \lt 10$.
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