Inequalities in Interval Notation and Distance Comparison

[MrNeWBiE]

Homework Statement

(1) Express the inequalities x≤3 and 1 ≤ x < 4 in interval notation.(2) Express in term of inequality: The distance between x and -3 is at least 5.

The Attempt at a Solution

(1) i don't know what he asking for ,,, can you explain it for me please

(2) is it " x+(-3)≥5 " ,,,, x≥2 ? right ?

in (2) he want me to find x or what is the story ?

 

[Mark44]

1. Look in your book for some examples of interval notation.
2. Absolute values are used to represent distance.

 

[MrNeWBiE]

first one ... done ,,,

2.
it's gone be " abs (x-3) ≥ 5 " then solve for it ?

 

[Mark44]

first one ... done ,,,

2.
it's gone be " abs (x-3) ≥ 5 " then solve for it ?

From you problem description, all that is asked for is the expression. You don't need to solve the inequality.

Your expression represents the distance between x and + 3.

Also, there's a key on the keyboard that you can use for absolute values - |

 

[MrNeWBiE]

O,O ... how is that ? in the question it's -3 ,,, why in absolute i make it |x+3|≥ 5 ?

 

[Mark44]

To find the distance, you subtract, so the distance from x to -3 is represented as is x - (-3).

 

[MrNeWBiE]

ahaa