What Does It Mean When an Inequality is a Contradiction or Has No Solution?

What Does It Mean When an Inequality is a Contradiction or Has No Solution?

Note:

Can an inequality have no solution? You bet it can! An inequality has no solution will always give you a contradiction, no matter what value you plug in for the variable. Watch this tutorial, and then try to make your own inequality with no solution!

Keywords:

  • definition
  • no solution
  • inequality
  • contradiction
  • never true
  • always false
  • solution set
  • empty
  • no answer
  • false

Background Tutorials

  • Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.

      • What's an Inequality?What's an Inequality?

      What's an Inequality?

      Inequalities come up all the time when you're working algebra problems. In this tutorial you'll learn what an inequality is, and you'll see all the common inequality symbols that you're likely to see :)

  • Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

      • What is a Variable?What is a Variable?

      What is a Variable?

      You can't do algebra without working with variables, but variables can be confusing. If you've ever wondered what variables are, then this tutorial is for you!

Further Exploration

  • Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

      • How Do You Solve an Equation with No Solution?How Do You Solve an Equation with No Solution?

      How Do You Solve an Equation with No Solution?

      Trying to solve an equation with variables on both sides of the equation? Figure out how to get those variables together and solve the equation with this tutorial! Surprise! Turns out, this equation has no solution. Check out this tutorial and see why!

  • Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

      • What is an Identity Inequality?What is an Identity Inequality?

      What is an Identity Inequality?

      And identity inequality is an inequality that it true no matter what values we plug in for the variable. Watch this tutorial and learn all about identity inequalities. Then see if you can make your own identity inequality complete with variables!