To see this let's look at your solution step by step:

5x+2y < 14

5x+2y-5x < -5x+14   <<< subtracted 5x from both sides

   2y  < -5x+14

    y  < -(5/2)x+7  <<< divided both sides by 2



Since you did not multiply or divide by a negative number (nor did you take reciprocals) no flip of the inequality should be made.   

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