Graphing Inecharacteristics on a Number Line
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We deserve to graph genuine numbers by representing them as points on the number line. For example, we have the right to graph "2" on the number line:
We deserve to also graph inefeatures on the number line. The adhering to graph represents the inequality x≤2. The dark line represents all the numbers that fulfill x≤2. If we pick any kind of number on the dark line and also plug it in for x, the inequality will certainly be true.
Using the Number Line to Solve Inequalities
We can use the number line to settle inecharacteristics containing , ≤, >, and also ≥. To fix an inehigh quality making use of the number line, change the inetop quality sign to an equal authorize, and fix the equation. Then graph the suggest on the number line (graph it as an open circle if the original inetop quality was ""). The number line have to now be divided into 2 areas -- one to the left of the point and also one to the ideal of the point
Next, pick a point in each region and also "test" it -- watch if it satisfies the inetop quality when plugged in for the variable. If it satisfies the inehigh quality, draw a dark line from the suggest right into that area, via an arrowhead at the end. This is the solution set to the equation: if one allude in the area satisfies the inetop quality, the whole area will certainly satisfy the inetop quality.
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Example: -3(x - 2)≤12Solve -3(x - 2) = 12:x - 2 = - 4x = - 2Graph x = - 2, utilizing a filled circle bereason the original inetop quality was ≤: