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 equal to the left side of the inequality and equal to the right side of the inequality.
STEP 2: Graph and 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 > or <
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.
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.
When Second curve? appears press ENTER again. When Guess? appears press ENTER again.
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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