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.
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Intersection of Graphs Method of Solving an Inequality This method uses graphing of functions to solve an inequality. STEP 1: Set STEP 2: Graph STEP 3: Locate any points of intersection.
The x-values of these points correspond to points that are the boundaries
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STEP 1: Press the 
button, then enter the left side of the inequality for
and the right side of the inequality
for
.
STEP 2: Next press the ZOOM, then 6. The graphs of the functions in a standard window are shown below.
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.
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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.
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When Second curve? appears press ENTER again. When Guess? appears press ENTER again.
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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 > ,
that is where the graph of is above the graph of
. is the steeper curve that graphs
first. Thus, the graph of is above (or greater than) the
graph of
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, = ;
when x > 7, > ;
and when x < 7, < .
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