## Introduction come Inequalities

Inequalities are offered to demonstrate relationships between numbers or expressions.

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### Key Takeaways

Key PointsAn inequality explains a relationship between two different values.The notation**number line**: A visual depiction of the set of actual numbers as a collection of points.

**inequality**: A statement that of two amounts one is specifically much less than or higher than another.

In mathematics, inequalities are supplied to compare the relative size of values. They deserve to be supplied to compare integers, variables, and also various various other algebraic expressions. A description of different varieties of inequalities follows.

### Strict Inequalities

A strict inequality is a relation that holds between two values as soon as they are different. In the same method that equations usage an equals sign, =, to present that 2 values are equal, inequalities use indications to display that two values are not equal and also to describe their relationship. The strict inequality symbols room

Strict inequalities differ from the notation *a* is no equal to

In the two varieties of strictly inequalities,

The definition of these symbols can be easily remembered by noting that the “bigger” side of the inequality price (the open side) encounters the bigger number. The “smaller” side of the prize (the point) faces the smaller sized number.

The above relations have the right to be demonstrated on a number line. Recall that the worths on a number line rise as you move to the right. The following therefore represents the relation

a b

In general, keep in mind that:

### Other Inequalities

In comparison to strict inequalities, there room two varieties of inequality relations that room not strict:

The notation*or equal to*

*or same to*

### Inequalities through Variables

In enhancement to mirroring relationships between integers, inequalities can be supplied to present relationships between variables and integers.

For example, take into consideration

x > 5

Note the the circle above the number 5 is open, indicating that 5 is not contained in feasible values that

For another example, think about

x leq 3

Note that the circle above the number 3 is filled, indicating that 3 is had in feasible values the

Inequalities room demonstrated by color in an arrow over the appropriate variety of the number heat to suggest the feasible values that

Each of this represents the relationship between two different expressions.

One valuable application of inequalities such together these is in problems that involve preferably or minimum values.

### Example 1

Jared has a boat with a maximum weight limit of 2,500 pounds. He wants to take as numerous of his girlfriend as feasible onto the boat, and he guesses the he and his friends weigh an median of 160 pounds. Exactly how many people can drive his boat at once?

This trouble can it is in modeled v the following inequality:

where *less than or equal to* the maximum weight of 2,500, i beg your pardon is the boat’s weight limit.

There are procedures that deserve to be complied with to fix an inequality such as this one. For now, the is essential simply to know the an interpretation of together statements and cases in i beg your pardon they might be applicable.

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## Rules for fixing Inequalities

Arithmetic operations can be provided to deal with inequalities because that all feasible values that a variable.