Graphing Inequalities on a Number Line
You are watching: The number line is a graph of the
We have the right to graph real numbers by representing them as points on the number line. For example, we can graph "2" on the number line:
We can also graph inequalities top top the number line. The complying with graph represents the inequality x≤2. The dark line represents every the number that fulfill x≤2. If we pick any number top top the dark line and plug it in because that x, the inequality will be true.
using the Number line to deal with Inequalities
We deserve to use the number heat to resolve inequalities include , ≤, >, and also ≥. To settle an inequality utilizing the number line, readjust the inequality sign to an equal sign, and solve the equation. Then graph the point on the number heat (graph it together an open up circle if the original inequality to be ""). The number line have to now be separated into 2 areas -- one come the left that the allude and one to the right of the point
Next, pick a allude in each an ar and "test" it -- check out if it satisfies the inequality as soon as plugged in because that the variable. If it satisfies the inequality, draw a dark line from the allude into that region, v an arrowhead at the end. This is the solution collection to the equation: if one point 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, utilizing a filled circle since the original inequality was ≤: