MHB Absolute Value Statements....2

AI Thread Summary
The discussion focuses on rewriting statements using absolute values. The first statement, "The number y is less than one unit from the number t," is correctly expressed as |t - y| < 1. The second statement regarding the sum of distances is clarified; the correct formulation is |a| + |b| ≥ |a + b|, rather than the initially proposed expression. Participants confirm that the rewording of the first statement is accurate. Overall, the thread emphasizes the importance of correctly applying absolute value concepts in mathematical expressions.
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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?
 
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RTCNTC said:
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" ?

RTCNTC said:
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:

$$|a|+|b|$$

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

$$|a+b|$$

And so we would write:

$$|a|+|b|\ge|a+b|$$
 
"The distance between y and t is less than 1 unit" ?

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

Yes?
 
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