Graphing Inequalities ~ above a Number Line

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

You are watching: Which number line represents the solution set for the inequality

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:

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Graph of the suggest 2

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.

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Graph that the Inequality x≤2The adhering to graph to represent the inequality x . Note that the open circle ~ above 2 mirrors that 2 is not a equipment to x .
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Graph that the Inequality x below 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 that the Inequality x≥2An inequality through a "≠" sign has a solution set which is every the actual numbers except a solitary point (or a variety of single points). Thus, come graph one inequality v a "≠" sign, graph the whole line v one suggest removed. Because that example, the graph the x≠2 watch like:
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Graph the the Inequality x≠2

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 ≤:

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