Graphing Inequalities on a Number Line

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Number LineRecall the a number line is a horizontal heat that has points which exchange mail to numbers. The points room spaced according to the value of the number they correspond to; in a number heat containing only whole numbers or integers, the points are equally spaced.

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:

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Graph the the suggest 2

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.

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Graph of the Inequality x≤2The complying with graph represents the inequality x . Note that the open circle on 2 shows that 2 is no a equipment to x .
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Graph the the Inequality x here are the graphs of x > 2 and x≥2, respectively:
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Graph of the Inequality x > 2
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Graph the the Inequality x≥2An inequality through a "≠" sign has a solution collection which is all the actual numbers other than a solitary point (or a number of single points). Thus, to graph an inequality with a "≠" sign, graph the entire line with one suggest removed. For example, the graph of x≠2 look at like:
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Graph the the Inequality x≠2

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 ≤:

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Graph that x = - 2Plug values into the equation -3(x - 2)≤12:Pick a suggest on the left the -2 (-3, because that example):-3(- 3 - 2)≤12 ?15≤12 ? No.Pick a point on the appropriate of -2 (0, because that example):-3(0 - 2)≤12 ?6≤12 ? Yes.Draw a dark line from -2 prolonging to the right, v an arrow at the end:
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Graph that -3(x - 2)≤12, or the x≥ - 2Thus, x≥ - 2.