compound inequality

Examples of compound inequality in the following topics:

• Compound Inequalities

  • A compound inequality involves three expressions, not two, but can also be solved to find the possible values for a variable.
  • The compound inequality $a < x < b$ indicates "betweenness"—the number $x$ is between the numbers $a$ and $b$.
  • For a visualization of this inequality, refer to the number line below.
  • Finally, it is customary (though not necessary) to write the inequality so that the inequality arrows point to the left (i.e., so that the numbers proceed from smallest to largest):
  • Solve a compound inequality by balancing all three components of the inequality

• Nonlinear Systems of Inequalities

  • A system of inequalities consists of two or more inequalities, which are statements that one quantity is greater than or less than another.
  • A nonlinear inequality is an inequality that involves a nonlinear expression—a polynomial function of degree 2 or higher.
  • The most common way of solving one inequality with two variables $x$ and $y$ is to shade the region on a graph where the inequality is satisfied.
  • Every inequality has a boundary line, which is the equation produced by changing the inequality relation to an equals sign.
  • If we have two inequalities, therefore, we shade in the overlap region, where both inequalities are simultaneously satisfied.

• Linear Inequalities

  • A linear inequality looks exactly like a linear equation, with the inequality sign replacing the equality sign.
  • For inequalities that contain variable expressions, you may be asked to solve the inequality for that variable.
  • A linear inequality looks like a linear equation, with the inequality sign replacing the equal sign.  
  • Solving the inequality is the same as solving an equation.  
  • Step 1, combine like terms on each side of the inequality symbol:

• 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.
  • Globally, income inequality has increased over the last few decades.
  • Given that economic theory points to a decline in income inequality over time, the recent increase has led many researchers to conclude that we may be starting a new inequality cycle .
  • The Kuznets curve depicts the relationship between inequality and income; after hitting a market peak, inequality will decrease as income increases.

• 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.
  • Although inequality is everywhere, there are many controversies and questions about inequality that sociologists are interested in, such as where did inequality come from?
  • Do we justify inequality?
  • Can we eliminate inequality?

• Introduction

  • 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.
  • Although inequality is everywhere, there are many controversies and questions about inequality that sociologists are interested in such as where did inequality come from?
  • Do we justify inequality?
  • Can we eliminate inequality?
  • We end with consequences of inequality and theories explaining global inequality.

• Graphs of Linear Inequalities

  • Graphing linear inequalities involves graphing the original line, and then shading in the area connected to the inequality.
  • Graphing an inequality is easy.
  • First, graph the inequality as if it were an equation.
  • Now if there is more than one inequality, start off by graphing them one at a time, just as was done with a single inequality.
  • To find solutions for the group of inequalities, observe where the area of all of the inequalities overlap.

• Evaluating Global Theories of Inequality

  • Social theorists think differently about global inequality based on their sociological perspective.
  • Marxists, by contrast, see global inequality as indicative of exploitation and consider it a detriment to society.
  • Whatever sociological theory one adopts to explain the existence of inequality, not all theorists consider inequality to be a problem that needs correction.
  • Those who evaluate global inequality and consider it to violate human rights may advocate for solutions to inequality using the language of social justice.
  • Protestors at Occupy Wall Street adhere to the position that income inequality is a detriment to society.

• Solving Problems with Inequalities

  • Speculate on the number of solutions of a linear inequality.
  • (Hint: Consider the inequalities x < x−6 and x ≥ 9. )
  • If any real number is added to or subtracted from both sides of an inequality, the sense of the inequality remains unchanged.
  • If both sides of an inequality are multiplied or divided by the same positive number, the sense of the inequality remains unchanged.
  • If both sides of an inequality are multiplied or divided by the same negative number, the inequality sign must be reversed (change direction) in order for the resulting inequality to be equivalent to the original inequality.

• 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.
  • Again, draw all the inequalities and shade in the area that each inequality covers.
  • If there is no intersection, then the two inequalities are either mutually exclusive, or one of the inequalities is a subset of the other.
  • Three inequalities are graphed.
  • There is no area which is shaded by all three inequalities, so the system of inequalities has no solution.