I am comfortable on how to use basic inequality. But how can I combine them together to get the desired region?

The desired region is intersection of the multiple inequalities (like in the image below)


enter image description here

  • $\begingroup$ The combination of inequalities may have empty intersection. You should identify which "half" of the plane each inequality corresponds to (one side of each line shown in your graph). The region which lies on the proper side of all those lines is the intersection of the half-planes, and represents the solutions (if any) of the system of linear inequalities. $\endgroup$
    – hardmath
    Mar 1, 2018 at 16:34

1 Answer 1


You are almost there. Use a pair of '{}' for each condition, like $$4x+3y\le12\left\{y\le2x\right\}\left\{y\ge-3\right\}\left\{x\le4\right\}.$$

truncated graph

Click on the picture to see the graph on Desmos.


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