Maths Olympiad Prep

Library / HMMT February /97 of 1302

HMMT February

Algebra Difficulty 4.7 AIME Find the answer

How many real solutions are there to the equation ∣∣∣∣x∣−2∣−2∣−2∣=∣∣∣∣x∣−3∣−3∣−3∣|||| x|-2|-2|-2|=|||| x|-3|-3|-3|?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

6. The graphs of the two sides of the equation can be graphed on the same plot to reveal six intersection points.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.