system of inequalities

(noun)

A set of inequalities with multiple variables, often solved with a particular specification of the values of all variables that simultaneously satisfies all of the inequalities.

Related Terms

Examples of system of inequalities in the following topics:

  • Solving Systems of Linear Inequalities

    • A system of inequalities is a set of inequalities with multiple variables, often solved with a particular specification of of the values of all variables that simultaneously satisfies all of the inequalities.
    • A system of inequalities can be solved graphically and non-graphically.
    • Often the easiest way to solve a system of linear inequalities is by graphing.
    • If all of the inequalities of a system fail to overlap over the same area, then there is no solution to that system.
    • There is no area which is shaded by all three inequalities, so the system of inequalities has no solution.

  • Nonlinear Systems of Inequalities

    • Systems of nonlinear inequalities can be solved by graphing boundary lines.
    • A system of inequalities consists of two or more inequalities, which are statements that one quantity is greater than or less than another.
    • This area is the solution to the system.
    • The limits of each inequality intersect at $(-1, 1)$ and $(2, 4)$.
    • Whereas a solution for a linear system of equations will contain an infinite, unbounded area (lines can only pass one another a maximum of once), in many instances, a solution for a nonlinear system of equations will consist of a finite, bounded area.

  • The Interactionist Perspective

    • The interactionist perspective on social inequality focuses on the way that micro-interactions maintain structural inequality.
    • For example, when a wife cleans up after her husband or leaves unquestioned an opinion of his that she disagrees with, it is an example of how inequality is reiterated in micro-interactions.
    • Interactionists consider the question of how power is exchanged in a situation.
    • When considering larger systems of inequality, interactionists look at the inequality between social roles.
    • All of these micro-interactions, which may seem trivial at the time, add up to status inequality, according to the interactionist.

  • Graphs of Linear Inequalities

    • The simplest inequality to graph is a single inequality in two variables, usually of the form: $y\leq mx+b$, where the inequality can be of any type, less than, less than or equal to, greater than, greater than or equal to, or not equal to.
    • To find solutions for the group of inequalities, observe where the area of all of the inequalities overlap.
    • These overlaps of the shaded regions indicate all solutions (ordered pairs) to the system.
    • This also means that if there are inequalities that don't overlap, then there is no solution to the system.
    • The overlapping shaded area is the final solution to the system of linear inequalities because it is comprised of all possible solutions to $y<-\frac{1}{2}x+1$ (the dotted red line and red area below the line) and $y\geq x-2$ (the solid green line and the green area above the line).  

  • Defining and Measuring Income Inequality

    • Income inequality uses the dispersion of capital to identify how economic inequality is defined among individuals in a given economy.
    • Income inequality utilizes the dispersion of capital to identify the way in which economic inequality is defined among a group of individuals in a given economy.
    • Hoover Index: Often touted as the simplest measurement to calculate, the Hoover Index derives the overall amount of income in a system and divides it by the population to create the perfect proportion of distribution in the system.
    • In a perfectly equal economy this would equate to income levels, and the deviance from this (on a percentile scale) is representative of the inequality in the system.
    • To simplify the information above, the basic concept behind measuring inequality is identifying an ideal and tracking any deviance from that ideal (which would be deemed the inequality of a given system).

  • Equations and Inequalities

    • In a set of simultaneous equations, or system of equations, multiple equations are given with multiple unknowns.
    • A solution to the system is an assignment of values to all the unknowns so that all of the equations are true.
    • An inequality is a relation that holds between two values when they are different.
    • These relations are known as strict inequalities.
    • In contrast to strict inequalities, there are two types of inequality relations that are not strict:

  • State-Centered Theories

    • According to state-centered theories of inequality, the government should regulate the distribution of resources to protect workers.
    • State-centered theories of inequality emphasize the role of governmental policy and economic planning in producing economic stratification.
    • Socialism includes a combination of public and private property, while under communist systems all property is publicly held and administered by the state.
    • A socialist economic system would consist of an organisation of production to directly satisfy economic demands and human needs.
    • This map of all states to declare themselves officially socialist at some point in history illustrates the spread of state-centered theories of inequality.

  • Linear Inequalities

    • This just means that you need to find the values of the variable that make the inequality true.  
    • There is only one rule that is different: When you multiply or divide each side of an inequality by a negative number, you must reverse the inequality symbol to maintain a true statement.
    • Step 1, combine like terms on each side of the inequality symbol:
    • Step 2, since there is a variable on both sides of the inequality, choose to move the $-4x$, to combine the variables on the left hand side of the inequality.
    • Notice the open circle means that the value of $4$ in not a solution to the inequality since $4>4$ is a false statement.  

  • How Income is Allocated

    • Recent growth in overall income inequality has been driven mostly by increasing inequality in wages and salaries.
    • Recent growth in overall income inequality has been driven mostly by increasing inequality in wages and salaries.
    • Globalization has contributed to some portion of rising inequality as jobs have moved to lower wage geographies, placing downward pressure on wages of higher cost of living countries.
    • However, economists view the impact of technological progress to outweigh the effect of globalization, as technology has effectively been substituted for more expensive wage labor.
    • Governments have a number of tools with which they can affect income distribution.

  • The Significance of Social Inequality

    • Sociologists study many types of inequality, including economic inequality, racial/ethnic inequality, and gender inequality.
    • Sociology has a long history of studying stratification and teaching about various kinds of inequality, including economic inequality, racial/ethnic inequality, gender inequality, and other types of inequality.
    • Do we justify inequality?
    • Can we eliminate inequality?
    • The water situation in Cape Verde, an island country in the central Atlantic, is a poignant illustration of global social inequality.