# Inequalities in Interval Notation and Distance Comparison

• MrNeWBiE
In summary, the first problem asks to express the inequalities x≤3 and 1 ≤ x < 4 in interval notation. The second problem asks for an expression for the distance between x and -3, which can be represented as |x-(-3)| ≥ 5.
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 ?

Last edited:
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 ?

MrNeWBiE said:
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 ?

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

ahaa

## 1. What are inequalities?

Inequalities are mathematical statements that compare two values or expressions, indicating which one is larger or smaller. They use symbols such as <, >, ≤, and ≥ to show the relationship between the two values.

## 2. How do you solve inequalities?

To solve inequalities, you follow the same steps as solving equations, but with one key difference. When multiplying or dividing by a negative number, you must flip the inequality sign. For example, if you multiply both sides of an inequality by -2, the greater than sign (> ) becomes a less than sign (< ).

## 3. What is the difference between an equation and an inequality?

An equation is a statement that shows the equality of two expressions, while an inequality shows the relationship between two expressions, indicating which one is larger or smaller. Inequalities use symbols such as <, >, ≤, and ≥, while equations use an equal sign (=).

## 4. How do you graph inequalities?

To graph inequalities, you first plot the boundary line, which is the line that separates the solutions from the non-solutions. The boundary line is either a solid or dotted line, depending on whether the inequality includes or excludes the line. Then, you shade the side of the line that represents the solutions to the inequality.

## 5. How are inequalities used in real life?

Inequalities are used in real life to compare and analyze data. For example, they can be used in budgeting to determine if someone's expenses are greater than their income. They are also used in fields such as economics and science to analyze relationships between variables and make predictions based on those relationships.

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