Absolute Value Statements....2

[mathdad]

Rewrite each statement using absolute values.

1. The number y is less than one unit from the number t.

y < | t - 1 |

2. The sum of the distances of a and b from the origin is greater than or equal to the distance of a + b from the origin.

| a + b - 0 | > or = | a + b - 0 |

Is this correct? If not, why not?

 

[MarkFL]

Rewrite each statement using absolute values.

1. The number y is less than one unit from the number t.

y < | t - 1 |

What if this is reworded to say the same thing, but in the form you had no trouble with:

"The distance between y and t is less than 1 unit" ?

2. The sum of the distances of a and b from the origin is greater than or equal to the distance of a + b from the origin.

| a + b - 0 | > or = | a + b - 0 |

Is this correct? If not, why not?

This isn't correct...the sum of the distances of a and b from the origin would be:

\(\displaystyle |a|+|b|\)

And the distance of the sum a + b from the origin is:

\(\displaystyle |a+b|\)

And so we would write:

\(\displaystyle |a|+|b|\ge|a+b|\)

 

[mathdad]

"The distance between y and t is less than 1 unit" ?

| t - y | < 1 or | y - t | < 1

Yes?