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Compound Inequality Calculator
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The compound inequality is that what has atleast two inequalities joined by either "and" or "or". These joining words determine the solution to the problem. If the inequality are joined with "and" the solution must include only the values that is valid with both the inequalities. If the inequality are joined with "or" the solution must include any value that is valid to atleast one inequality. Before we start with compound inequalities we must have hand on single inequality equations.  Inequalities Tool helps to understand and solve these type of problems.


The compound inequalities Calculator is a compound inequality solver to calculate the variable value for any compound inequalities. You just have to enter the two inequalities in the block provided for compound inequality calculator and select a proper conjunction for it to get your answer instantly even with a plot of solutions on number line. It is also known as compound inequalities solver
Two default inequalities are given in the calculator below. The calculator will solve the two inequalities to get the solutions. A number line is drawn by the resultant solutions when you click on "Solve".
 

Steps for Compound Inequality Calculator

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Step 1 :  

Go through the given problem. Observe whether it has atleast two inequalities joined by "and" or "or".



Step 2 :  

Solve each inequality seperately and get the solutions of each.



Step 3 :  

Plot the solutions on number line and analyze it.



Problems on Compound Inequality Calculator

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  1. Represent the inequality 4x+2 $\geq$ 3 and  x+3 < 5 on number line.


    Step 1 :  

    The given inequality is 4x+2 $\geq$ 3 and x+3 < 5



    Step 2 :  

    Lets solve the two inequqlities seperately
    4x+2 $\geq$ 3
    4x $\geq$ 3-2
    4x $\geq$ 1
    => x $\geq$ $\frac{1}{4}$

    x+3 < 5
    x < 5-3
    => x < 2  

    The solution is x$\geq$ $\frac{1}{4}$ and x<2.



    Step 3 :  

    The graph on number line is


    compound inequality graph



    Answer  :  

    Hence the solution is x$\geq$ $\frac{1}{4}$ and x<2 implies $\frac{1}{4}$ $\leq$ x < 2.



  2. Solve the inequality 2+5x < 5 or x-3 < 5 on number line.


    Step 1 :  

    The given inequality is 2+5x < 5 0r x-3 < 5.



    Step 2 :  

    Lets solve the two inequalities seperately
    2+5x < 5
    5x < 5 - 2
    x < $\frac{3}{5}$

    x-3 < 5
    x < 5-3
    => x < 2  

    Hence the solution is x < $\frac{3}{5}$ 0r x < 2.



    Step 3 :  

    Lets take one of the two solutions x <  $\frac{3}{5}$. The graph on number line is


    compound inequality example graph



    Answer  :  

    Hence the solution is x < $\frac{3}{5}$ 0r x < 2.



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