Plot 8/10 On Number Line
Graphing Inequalities on a Number Line
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- This Solver (Plot a number on a number line) was created by by ichudov(507): View Source, Show, Put on YOUR site About ichudov: I am not a paid tutor, I am the owner of this web site. Plot a number on a number line. Plot on the number line.
- Create a line plot that displays the data. A girl measures pictures of animals in her classroom. This chart shows the length, in inches, of each picture. Pictures length (in.) Giraffe 4 ½ Turtle 5 Polar Bear 5 ½ Gorilla 4 Whale 6 Alligator 6 ¼ Penguin 5 ¾ Lion 6 ½ Create a line plot that displays the data.
Recall that a number line is a horizontal line that has points which correspond to numbers. The points are spaced according to the value of the number they correspond to; in a number line containing only whole numbers or integers, the points are equally spaced.
We can 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 on the number line. The following graph represents the inequality x≤2. The dark line represents all the numbers that satisfy x≤2. If we pick any number on the dark line and plug it in for x, the inequality will be true.
The following graph represents the inequality x < 2. Note that the open circle on 2 shows that 2 is not a solution to x < 2.
Here are the graphs of x > 2 and x≥2, respectively:
An inequality with a '≠' sign has a solution set which is all the real numbers except a single point (or a number of single points). Thus, to graph an inequality with a '≠' sign, graph the entire line with one point removed. For example, the graph of x≠2 looks like:
Using the Number Line to Solve Inequalities
We can use the number line to solve inequalities containing <, ≤, >, and ≥. To solve an inequality using the number line, change the inequality sign to an equal sign, and solve the equation. Then graph the point on the number line (graph it as an open circle if the original inequality was '<' or '>'). The number line should now be divided into 2 regions -- one to the left of the point and one to the right of the point
Next, pick a point in each region and 'test' it -- see if it satisfies the inequality when plugged in for the variable. If it satisfies the inequality, draw a dark line from the point into that region, with an arrow at the end. This is the solution set to the equation: if one point in the region satisfies the inequality, the entire region will satisfy the inequality.
Example: -3(x - 2)≤12
Solve -3(x - 2) = 12:
x - 2 = - 4Graph x = - 2, using a filled circle because the original inequality was ≤:
x = - 2
Plot The Numbers Number Line
Plug values into the equation -3(x - 2)≤12:
Pick a point on the left of -2 (-3, for example):Draw a dark line from -2
-3(- 3 - 2)≤12 ?
15≤12 ? No.
Pick a point on the right of -2 (0, for example):
-3(0 - 2)≤12 ?
6≤12 ? Yes.
extending to the right, with an arrow at the end: