Inequalities are widely used when stating an ordered relation between any two numbers or their two expressions of algebra. Five ways are there that can support providing mathematical relations between two distinct algebraic expressions. In this study, focus will be given to the ways for interpretation of solutions to inequalities. Furthermore, within the study, notable focus is given to determining the combination of inequalities, graphing inequalities and linear equalities.

## Understanding All About On Solutions of Inequalities

Delving into the topic it needs to be noticed that inequalities majorly provide an expression that caters for providing an effective relationship between two expressions of algebra. It can also show relationships between integers as well as variables. Furthermore, in this study of solutions to inequalities, it is noticed that there are five respective relationships stated by signs of inequalities. In terms of graphical representation, it is noticed that with value to the functions of x, the critical values are plotted on a two-dimensional graph on the abscissa or x-axis. In mathematics, the notion of inequalities majorly depends on determining the relationship that determines, greater than, less than, less than equal to, not equal to and as well as greater than equal to. It can also be stated that mathematical analysis often depends on the notions of equalities.

## What Are Inequalities?

The term inequality intends to refer to a statement of relationships between two distinct values in order to conduct an effective comparison. Moreover, in the aspects or proving of theorems, such notions as equalities are crucial as it supports scientists in determining the mathematical analysis. One such example is known as “inequality of Cauchy-Schwarz”, that provides in establishing a true relationship between the two algebraic expressions. This has also been noticed that relationships can be stated with the help of five conditions. Moreover, it is noted that the inequalities can be successively represented with the graph by evaluating the critical value of functions of x within a given equation.

## Combinations of Inequalities

The term “combinations of inequalities” is a widely used term in chapters of algebra that provides assistance in satisfying both the algebraic inequalities. Moreover, it refers to a condition, where there lies a common number that will be present in both the sets associated with the solutions. Therefore, in simple terms, it means that both algebraic inequalities are successively satisfied and as well as their values within the point of intersection for two solution sets. The set can be represented as a notation of intervals such as, “(-2, 4)” respectively. In addition to this, the condition can be stated as “double inequality”.

## Graphing Inequalities

Based on graphical representation, several steps can be applied, but primarily three necessary steps are concerned that are as follows.

- The first step caters to the rearrangements of the ordinate of y on the left side of the equation leaving all the terms on right.
- Afterwards, values associated with the ordinate or y are plotted on the graph,
- Finally, the regions concerning the plotted values of the ordinate are to be defined by the shaded regions.

## Linear Inequalities

Delving into the notions associated with the inequalities, linear inequality posits equal importance in its application. The linear equation refers to a solving system without focusing on points of intersection. In addition to these, it can be stated that the set of solutions refers to a region that intends to satisfy the linear equalities. Moreover, catering to the study, it is noticed that the better way to solve linear inequalities is by graphical representations.

## Graphically Solving Of System of Linear Inequalities

The best way to acknowledge this is through graphical representations in solving equations associated with linear equalities. The first step is solving inequality for ordinate and then followed by treating the linear equations that can be represented on lines of solid or dashed. It is to be noted that the strict inequalities present dashed lines.

### Conclusion

Reaching this far in the study, it can be easily noticed that the inequalities are essential in providing a relationship between two expressions of algebra. Moreover, the inequalities can also be represented on the 2-dimensional graphs but effectively determine the value associated with abscissa or x-axis. Delving into the study, it can be acknowledged that solving inequalities provides a comparison to the values associated with relative sizes. It can be used to successively compare variables, integers as well as many algebraic expressions.