How Do You Solve an Inequality With Variables on Both Sides?

How Do You Solve an Inequality With Variables on Both Sides?

Note:

Solving an inequality for a variable? Just perform the order of operations in reverse! Don't forget that if you multiply or divide by a negative number, you MUST flip the sign of the inequality! That's one of the big differences between solving equalities and solving inequalities.

Keywords:

  • problem
  • inequality
  • solve
  • like terms
  • variables on both sides
  • flip inequality
  • negative
  • solve by division
  • solve by addition
  • division property of inequality
  • addition property of inequality
  • flip inequality
  • flip
  • 1 variable
  • set builder notation
  • two operations

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!

  • Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

      • What are Like Terms?What are Like Terms?

      What are Like Terms?

      Combining like terms together is a key part of simplifying mathematical expressions, so check out this tutorial to see how you can easily pick out like terms from an expression

  • Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.

      • How Do You Write Inequalities in Set Builder Notation?How Do You Write Inequalities in Set Builder Notation?

      How Do You Write Inequalities in Set Builder Notation?

      Need some extra practice converting solution phrases into set builder notation? This tutorial was made for you! Follow along as this tutorial shows you how to dissect each phrase and turn it into a solution in set builder notation.

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

      • How Do You Solve and Graph a Two-Step Inequality?How Do You Solve and Graph a Two-Step Inequality?

      How Do You Solve and Graph a Two-Step Inequality?

      Solving an inequality for a variable? Just perform the order of operations in reverse! Don't forget that if you multiply or divide by a negative number, you MUST flip the sign of the inequality! That's one of the big differences between solving equalities and solving inequalities.

      • How Do You Solve an Inequality with Negative Numbers Using Division?How Do You Solve an Inequality with Negative Numbers Using Division?

      How Do You Solve an Inequality with Negative Numbers Using Division?

      Solving an inequality for a variable? Just perform the order of operations in reverse! Don't forget that if you multiply or divide by a negative number, you MUST flip the sign of the inequality! That's one of the big differences between solving equalities and solving inequalities.

      • What's the Division Property of Inequality?What's the Division Property of Inequality?

      What's the Division Property of Inequality?

      Ever wondered what rules you're allowed to follow when you're working with inequalities? Well, one of those rules is called the division property of inequality, and i

Further Exploration

  • Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.

      • How Do You Solve a Word Problem Using a Multi-Step Inequality?How Do You Solve a Word Problem Using a Multi-Step Inequality?

      How Do You Solve a Word Problem Using a Multi-Step Inequality?

      This tutorial provides a great real world application of math. See how to turn a word problem into an inequality. Then solve the inequality by performing the order of operations in reverse. Don't forget that if you multiply or divide by a negative number, you MUST flip the sign of the inequality! That's one of the big differences between solving equalities and solving inequalities.

      • How Do You Solve a Word Problem Using an Inequality With Variables on Both Sides?How Do You Solve a Word Problem Using an Inequality With Variables on Both Sides?

      How Do You Solve a Word Problem Using an Inequality With Variables on Both Sides?

      This tutorial provides a great real world application of math. See how to turn a word problem into an inequality. Then solve the inequality by performing the order of operations in reverse. Don't forget that if you multiply or divide by a negative number, you MUST flip the sign of the inequality! That's one of the big differences between solving equalities and solving inequalities.

  • 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).