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Absolute Value Prove

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Absolute Value Prove

Postby nycmath » Fri Aug 14, 2026 4:59 pm

Precalculus
David Cohen
Edition 3
Chapter 1, Section 1.2

67. Show that | a + b + c | ≤ | a | + | b | + | c | for all real numbers a, b, and c.
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Re: Absolute Value Prove

Postby Eigenvalue » Fri Aug 14, 2026 6:28 pm

|a+b+c|=|(a+b)+c|
|(a+b)+c|[tex]\le[/tex]|a+b|+|c|
|a+b|=|a|+|b|
|a+b+c|[tex]\le[/tex]|a|+|b|+|c|

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Re: Absolute Value Prove

Postby nycmath » Fri Aug 14, 2026 6:45 pm

Eigenvalue wrote:|a+b+c|=|(a+b)+c|
|(a+b)+c|[tex]\le[/tex]|a+b|+|c|
|a+b|=|a|+|b|
|a+b+c|[tex]\le[/tex]|a|+|b|+|c|


Can you explain each step when time allows?

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