The Intersection of Graphs Method can be used to find solutions for an inequality. To solve the inequality 2x - 3 > x + 4 using this method, follow the steps below.

 

Intersection of Graphs Method of Solving an Inequality

This method uses graphing of functions to solve an inequality. 

STEP 1: Set Y sub 1 equal to the left side of the inequality and Y sub 2 equal to the right side of the inequality.

STEP 2: Graph Y sub 1 and Y sub 2 in the same viewing rectangle. 

STEP 3: Locate any points of intersection.  The x-values of these points correspond to points that are the boundaries where Y sub 1 > Y sub 2 or Y sub 1 < Y sub 2

 

STEP 1: Press the button, then enter the left side of the inequality forY sub 1 and the right side of the inequality forY sub 2.

Screen Picture of TI-83 Calculator

STEP 2: Next press the ZOOM, then 6. The graphs of the functions in a standard window are shown below.

Screen Picture of TI-83 Calculator

STEP 3: The intersection point of the two lines is not visible using a standard window. Zoom out once so that the intersection point is visible.  (Remember to press ENTER for the zoom out to happen).  Now press the 2nd key, then TRACE [CALC], then select 5:intersection.

Screen Picture of TI-83 Calculator Screen Picture of the TI-83 Calculator


If the cursor is not near the intersection point, move it close to the point of intersection using the ARROW keys and then press ENTER.

Screen Picture of TI-83 Calculator Screen Picture of TI-83 Calculator

When Second curve? appears press ENTER again.   When Guess? appears press ENTER again.

Screen Picture of TI-83 Calculator Screen Picture of TI-83 Calculator Screen Picture of TI-83 Calculator
 

The final screen shows that the intersection point is (7,11). Thus X = 7 is where 2x -3 = x + 4. To determine where 2x -3 > x + 4, see where Y sub 1 > Y sub 2, that is where the graph of Y sub 1 is above the graph of Y sub 2 . Y sub 1 is the steeper curve that graphs first. Thus, the graph of Y sub 1 is above (or greater than) the graph of Y sub 2 when x > 7. Thus x > 7 is the solution to the above inequality.

The solution x > 7 can be confirmed by looking at the table of values. Press 2nd and then GRAPH [TABLE]. As visible below, when x = 7, Y sub 1 = Y sub 2; when x > 7, Y sub 1 > Y sub 2; and when x < 7, Y sub 1 < Y sub 2.



© 2001-2007 Macon State College.  All rights reserved.