What is the number of distinct positive integer values for x that satisfy the inequality $|x+5|<x$ ?

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To determine how many distinct positive integer values of x satisfy the inequality |x+5|

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Comments

ChristopherMar 27, 2025

thank you very much!

PatrickApr 8, 2024

thanks!

LamanSep 28

easiest way to see it is to just test x=1 and x=10, both fail immediately. once you realize LHS is always positive and RHS has to be bigger, positive x only, you can kill it fast. answer is 0, took me 30 sec.

VedikaOct 9

wait, why does LHS always being positive matter here?

What this question tests

What it tests

Your ability to solve and combine linear inequalities and reason about ranges of values.

Common trap

Failing to flip the inequality sign when multiplying or dividing by a negative, or missing an inclusive/exclusive endpoint.

What is the number of distinct positive integer values for x that satisfy the inequality ∣x+5∣<x|x+5|<x∣x+5∣<x?