# Inequalities questions

## 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 ?

Last edited:

Related Precalculus Mathematics Homework Help News on Phys.org
Mark44
Mentor
1. Look in your book for some examples of interval notation.
2. Absolute values are used to represent distance.

first one ... done ,,,

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

Mark44
Mentor
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 - |

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

Mark44
Mentor
To find the distance, you subtract, so the distance from x to -3 is represented as is x - (-3).

ahaa