Graphing Inequalities ~ above a Number Line
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We deserve to graph real numbers through representing them as points ~ above the number line. For example, we can graph "2" top top the number line:
We can also graph inequalities top top the number line. The complying with graph to represent the inequality x≤2. The dark line represents every the number that meet x≤2. If we pick any number ~ above the dark line and also plug that in because that x, the inequality will be true.
using the Number line to fix Inequalities
We have the right to use the number line to deal with inequalities comprise , ≤, >, and ≥. To solve an inequality utilizing the number line, change the inequality authorize to an same sign, and solve the equation. Climate graph the suggest on the number line (graph it together an open circle if the initial inequality was ""). The number line should now be split into 2 regions -- one come the left that the allude and one come the appropriate of the point
Next, pick a point in each an ar and "test" it -- check out if it satisfies the inequality once plugged in because that the variable. If that satisfies the inequality, draw a dark heat from the point into that region, with an arrow at the end. This is the solution set to the equation: if one suggest in the an ar satisfies the inequality, the entire region will meet the inequality.
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Example: -3(x - 2)≤12Solve -3(x - 2) = 12:x - 2 = - 4x = - 2Graph x = - 2, making use of a to fill circle because the initial inequality to be ≤: