Problem: Jill and also Juan to be at Amy"s house. Jill rode she bicycle 3 miles west of Amy"s house, and Juan rode his bike 3 miles eastern of Amy"s house. Who traveled a better distance from Amy"s home - Jill or Juan?

Solution: Jill and Juan both travel the exact same distance native Amy"s house due to the fact that each traveled 3 mile (in opposite directions).

You are watching: How many different integers can have the same absolute value

The problem above can be fixed using integers. Traveling 3 miles west can be stood for by -3 (pronounced negative 3). Traveling 3 miles eastern can be stood for by +3 (pronouncedpositive 3). Amy"s house can be represented by the integer 0.

Two integers that are the same distance native zero in the contrary directions space called **opposites**. The integers +3 and -3 are opposites since they are each 3 units from zero.

**The absolute worth of an integer is its street from zero top top the number line.** The absolute value of +3 is 3, and the absolute value of -3 is 3. Thus, the contrary integers have the very same absolute value. Mathematicians use the price || for pure value. Let"s look at part examples.

Example 1: uncover the absolute worth of +3, -3, +7, -5, +9, -8, +4, -4. You might refer come the number line below.

Solution:

|+11| = 11 | |+17| = 17 | |

|-9| = 9 | |-19| = 19 | |

|+14| = 14 | |+20| = 20 | |

|-10| = 10 | |-20| = 20 |

Remember that as soon as we find the absolute worth of one integer, we space finding its street from 0 ~ above the number line. Opposite integers have actually the very same absolute value since they are both the very same distance from 0. Also, friend will notice that acquisition the absolute value of an integer strips the authorize from the integer.

Example 2: find the absolute worth of: +11, -9, +14, -10, +17, -19, +20, -20. Friend may expand the number line listed below to help you resolve this problem.

Solution:

|+11| = 11 | |+17| = 17 | |

|-9| = 9 | |-19| = 19 | |

|+14| = 14 | |+20| = 20 | |

|-10| = 10 | |-20| = 20 |

Example 3: usage the number line listed below to fix this problem: |x| = 5

Solution: This problem asks united state to uncover all integers that room a distance of 5 systems from zero on the number line. Us let x stand for all integers that accomplish this condition.

The integer +5 is 5 systems from zero on the number line, and the integer -5 is additionally 5 systems from zero ~ above the number line. For this reason both +5 and -5 meet the provided condition.

x = +5 and x = -5, or we can write x = +5, -5

Summary: The absolute worth of an essence is its street from zero top top the number line. The notation |x| is used for the absolute worth of one unknown integer that satisfies a offered condition.

### Exercises

Directions: read each concern below. Click once in response BOX and type in her answer; climate click ENTER. After girlfriend click ENTER, a article will show up in the results BOX to indicate whether your answer is correct or incorrect. To begin over, click CLEAR.

1. | Find the absolute worth of -6.ANSWER BOX: RESULTS BOX: |

2. | Find |+15|ANSWER BOX: RESULTS BOX: |

3. | Find |-31|ANSWER BOX: RESULTS BOX: |

4.See more: 7.35X10^22 Kg To G Ravity - Solar System Homework #1 Answers | Find |+31|ANSWER BOX: RESULTS BOX: |

5. | How many values that y will certainly you gain when you settle |y| = 29?ANSWER BOX: RESULTS BOX: |