How to Solve Double Inequalities

Solve fractional inequalities with a graphing calculator.
••• Hemera Technologies/Photos.com/Getty Images

Double inequalities may appear too intimidating at first to solve because there are three sides to the equation, but, if you follow the step-by-step guide that provided below you may find them a little less intimidating and a lot easier to solve.

Solving Double Inequalities

    Begin by just taking a look at your double inequality before you actually start doing any mathematical processes to the double inequality.

    Start solving your double inequality for x by doing all processes to all three parts of the equation. So, just like you would do all processes to both sides of the equation when solving for x with a "regular" equation, you need to do all processes to all sides of the double inequality. For example, if you had the following double equality, 3<2x+8<20, then you would need to do all processes that you do to the middle to both the left and the right as well. For the following steps I will guide you through solving this particular double inequality.
    Remember: When solving any kind of equation for a value of x you need to follow the order of operations in reverse, which means that you need to do the processes in the following order: subtraction/addition, multiplication/division, exponents, parentheses. One easy way to remember the order of operations is by remembering the word PEMDAS, Parentheses, Exponents, Multiplication/Division (these two operations are interchangeable), Addition/Subtraction (these two operations are also interchangeable). Now when you are solving an equation, or in this case, a double inequality, for x, simply follow PEMDAS backwards.

    Subtract eight from all three sides of the equation. This is what you should be left with when you start with the double inequality 3<2x+8<20: -5<2x<12

    Divide all sides of the inequality by two. This is the solution to your double inequality: -2.5<x<6

    Remember that if you have to divide or multiply by a negative number in order to get your solution that you need to flip both inequality symbols. If you forget to flip the inequality symbols when multiplying or dividing by a negative number you will not only have the wrong answer, you will have an impossible answer. For example: 3<-2x+8<20 -5<-2x<12 2.5x>-6.

Related Articles

How to Find Double Square Roots
How to Solve Algebraic Equations With Double Exponents
What Are Double Angle Identities?
How to Identify Prime Polynomials in Algebra
How to Find the Radius of a Cylinder When Given the...
How to Find the Intersection of Two Linear Equations
How to Find Double Square Roots
What Are the X-Intercept & Y-Intercept of a Linear...
When Do You Flip the Inequality Sign?
Methods for Factoring Trinomials
How to Add Parentheses to Make a Statement True
How to Divide Polynomials By Monomials
How to Solve 3-Variable Linear Equations on a TI-84
How to Find the Domain of a Function Defined by an...
How to Factorize Equations
How to Find All Real Solutions of an Equation
How to Solve a Math Problem Using PEMDAS
How to Solve Binomial Equations by Factoring
How to Create Linear Equations
How to Simplify Exponents

Dont Go!

We Have More Great Sciencing Articles!