# Solving Equations Numerically Figure 2.1a Rename the independent variable x if necessary. For Figure 2.1a, Set up the table. Set up the column for the.

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Solving Equations Numerically Figure 2.1a Rename the independent variable x if necessary. For Figure 2.1a, Set up the table. Set up the column for the independent variable, x, by setting a minimum integer value 0 and increments of 1 for integers. 2nd TBLSET 1 0 ENTER (Minimum number in the table is 0.) (Values of independent variable are increasing by 1.) Set the calculator to perform the operations automatically. ENTER ▼ Technology 2.1 1 of 3

Solving Equations Numerically Figure 2.1b For Figure 2.1b, Set up the second column to be the expression on the left side by entering the left expression of the equation, 2x + 3, in Y1. 5 ENTER + 3+2Y= Set up the third column to be the expression on the right side by entering the right expression of the equation, x + 5, in Y2. Technology 2.1 X,T, ,n 2 of 3

Solving Equations Numerically Figure 2.1c For Figure 2.1c, View the table. Move beyond the screen to view additional rows by using the up and down arrows. The solution is the x-value that results in equal Y1 and Y2 values. The solution of 2x + 3 = x + 5 is 2 because 7 = 7. 2ndTABLE Technology 2.1 3 of 3

Solving Equations Graphically Solve 2x + 3 = x + 5 graphically. Figure 2.4a Rename the independent variable x if necessary. Enter the expression on the left side of the equation, 2x + 3, as Y1. Enter the expression on the right side of the equation, x + 5, as Y2. +3 5+ 2Y= ENTER Technology 2.4 X,T, ,n 1 of 3 For Figure 2.4a,

Solving Equations Graphically Solve 2x + 3 = x + 5 graphically. Figure 2.4b Graph the equations. (In this case, we will use the standard window.) TRACE ENTER CALC ZOOM 2nd5 6 Find the intersection of the graphs. First trace the graph. Use the arrow keys to find the intersection. If the intersection cannot be found by tracing, use INTERSECT, option 5, under the CALC menu. Technology 2.4 2 of 3 For Figure 2.4b, Y1 = 2x + 3 Y2 = x + 5 (-10, 10, -10, 10)

Solving Equations Graphically Solve 2x + 3 = x + 5 graphically. Figure 2.4c The solution is the x-value of the intersection point and is stored in x. The y-coordinate of the point of intersection is the value obtained for both the left side (Y1) and the right side (Y2) and is also stored. We can use this feature to check whether Y1 equals Y2. Quit the graph screen and enter x. VARSENTER VARS ENTERQUIT 2111► 2nd Enter Y1 and Y2. ► Since x = 2 when 7 = 7 (or Y1 = Y2), the solution of 2x + 3 = x + 5 is 2. For Figure 2.4c, Technology 2.4 X,T, ,n 3 of 3

Graphing Number Lines Figure 2.6a For Figure 2.6a, Enter the inequality x < 5 in Y1. The inequality symbols are found under the TEST menu. The “less than” symbol is option 5. Y= For Figure 2.6b, Graph the number line. The calculator will test the inequality for x-values and graph an ordered pair (x, 1) for a true inequality and (x, 0) for a false inequality. Figure 2.6b ZOOM6 52nd5TEST Technology 2.6 X,T, ,n 1 of 2 (-10, 10, -10, 10)

Graphing Number Lines Figure 2.6c For Figure 2.6c, Trace and use the arrow keys to display the coordinates graphed. To check the lower bound of a number line, 5, enter the value while tracing. TRACEENTER5 If the lower bound is a solution of the inequality, it will have a y-coordinate of 1. If the lower bound is not a solution of the inequality, it will have a y-coordinate of 0. For x < 5, the lower bound is not a solution and is graphed as (5, 0). Technology 2.6 2 of 2 (-10, 10, -10, 10)

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