Mathbound
Sign up

AMC / AIME · Absolute Value · AIME / USAJMO / AMO

Absolute Value: (Proof track.) Give a complete justification. Find the least math such that math for all math.

Cases and graphs.

Try the problem

**(Proof track.)** Give a complete justification. Find the least cc such that ∣x−2∣+∣x−7∣≤c|x-2|+|x-7|\le c for all x∈[0,10]x\in[0,10].

Hint and answer

Concept to use

Piecewise contests.

Hint

Break the real line at the expression's zeroes and justify each interval.

Answer

11

More Absolute Value problems

Practice more with the free Absolute Value worksheet generator, or browse the full problem library.