Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Write Expression Without Absolute Values

Rewrite each expression in a form that does not contain absolute values.
How is this done? 

(a) | pi - 4 | + 1

(b) | x - 5 | given that x > or = 5

(c) | t - 5 | given that t < 5.

Last edited by mathxyz (2024-05-25 20:33:58)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Write Expression Without Absolute Values

Each one contains a calculation.  If the result is positive or zero then the absolute sign is redundant; you can simply leave it out. If the result is negative then the result must be made positive (by multiplying by minus 1).  In all of these you can decide whether the result is + or - .

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Write Expression Without Absolute Values

Each one contains a calculation.  If the result is positive or zero then the absolute sign is redundant; you can simply leave it out. If the result is negative then the result must be made positive (by multiplying by minus 1).  In all of these you can decide whether the result is + or - .

Bob

Can the definition of absolute value be used to solve these?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Write Expression Without Absolute Values

Of course. No other way.  The positive value of a calculation is the same if its positive or zero and otherwise switch the sign.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Write Expression Without Absolute Values

Of course. No other way.  The positive value of a calculation is the same if its positive or zero and otherwise switch the sign.

Bob

Ok.