How to Graph Single Variable Inequalities

How to Graph Single Variable Inequalities?

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Steps to graphing single–variable inequalities

  • Inequality is comparable to equations and employs symbols such as “less than” (\(<\)) and “greater than” (\(>\)).
  • To find the answer for inequalities, you must isolate the variable. (as in equations)
  • To graph the inequality, figure out its value on a number line.
  • For less than or greater than you need to draw an open circle on the variable’s value.
  • If it also has an equal sign, you must then use a filled circle.
  • Put a line to the right or to left for greater or less than.

To understand how to graph inequalities better, below are some examples

Example one:
Make a graph for \(x > 5\).
Answer:
As the variable is higher than \(5\), you must find \(5\) and draw an open circle above it. Afterward, draw a line to the right.
 Graph Single Variable Inequalities

Example two:
Make a graph for \(x \ < \ 4\).
Answer:
As the variable is lower than \(4\), you must find \(4\) and then draw an open circle above it. Afterward, draw a line to the left.

Graph Single Variable Inequalities1

Free printable Worksheets

Exercises for Graphing Single Variable Inequalities

1) Make a graph for \(x \ > \ -2\)

2) Make a graph for \(x \ ≤ \ 1\)

3) Make a graph for \(x \ + \ 3 \ ≥ \ -2\)

4) Make a graph for \(x \ - \ 9 \ ≤ \ -10\)

5) Make a graph for \(x \ > \ -4\)

6) Make a graph for \(x \ < \ 5\)

7) Make a graph for \(x \ - \ 6 \ < \ -3\)

8) Make a graph for \(x \ - \ 7 \ < \ -5\)

9) Make a graph for \(x \ + \ 11 \ > \ 13\)

10) Make a graph for \(x \ - \ 6 \ ≤ \ -9\)

 

1) Make a graph for \(x \ > \ -2\)

Since the variable (\(x\)) is greater than \(3\), first, we should find \(3\), then draw an open circle above it and draw a line to the right.
Single Variable Inequalities

2) Make a graph for \(x \ ≤ \ 1\)

As the variable is lower than or equal to \(1\), you must find \(1\) and then draw a close circle above it. Afterward, draw a line to the left.
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3) Make a graph for \(x \ + \ 3 \ ≥ \ -2\)

In this example first, we must isolate the variable. To do this subtract \(3\) from both sides:
\(x \ + \ 3 \ - \ 3 \ ≥ \ -2 \ - \ 3 \ ⇒ \ x \ ≥ \ -5\)
Now, Since the variable (\(x\)) is greater than or equal to \(-5\), we must find \(-5\) and then draw a close circle above it. Afterward, draw a line to the right.
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4) Make a graph for \(x \ - \ 9 \ ≤ \ -10\)

In this example first, we must isolate the variable. To do this add \(9\) to both sides:
\(x \ - \ 9 \ + \ 9 \ ≤ \ -10 \ + \ 9 \ ⇒ \ x \ ≤ \ -1\)
Now, Since the variable (\(x\)) is lower than or equal to \(-1\), we must find \(-1\) and then draw a close circle above it. Afterward, draw a line to the left.
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5) Make a graph for \(x \ > \ -4\)

Since the variable (\(x\)) is greater than \(-4\), first, we should find \(-4\), then draw an open circle above it and draw a line to the right.
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6) Make a graph for \(x \ < \ 5\)

As the variable is lower than \(5\), you must find \(5\) and then draw an open circle above it. Afterward, draw a line to the left.Single Variable Inequalities
7) Make a graph for \(x \ - \ 6 \ < \ -3\)
In this example first, we must isolate the variable. To do this add \(6\) to both sides:
\(x \ - \ 6 \ + \ 6 \ < \ -3 \ + \ 6 \ ⇒ \ x \ < \ 3\)
Now, Since the variable (\(x\)) is lower than \(3\), we must find \(3\) and then draw an open circle above it. Afterward, draw a line to the left.
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8) Make a graph for \(x \ - \ 7 \ < \ -5\)
In this example first, we must isolate the variable. To do this add \(7\) to both sides:
\(x \ - \ 7 \ + \ 7 \ < \ -5 \ + \ 7 \ ⇒ \ x \ < \ 2\)
Now, Since the variable (\(x\)) is lower than \(2\), we must find \(2\) and then draw an open circle above it. Afterward, draw a line to the left.
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9) Make a graph for \(x \ + \ 11 \ > \ 13\)
In this example first, we must isolate the variable. To do this subtract \(11\) from both sides:
\(x \ + \ 11 \ - \ 11 \ > \ 13 \ - \ 11 \ ⇒ \ x \ > \ 2\)
Now, Since the variable (\(x\)) is greater than \(2\), we must find \(2\) and then draw an open circle above it. Afterward, draw a line to the right.
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10) Make a graph for \(x \ - \ 6 \ ≤ \ -9\)
In this example first, we must isolate the variable. To do this add \(6\) to both sides:
\(x \ - \ 6 \ + \ 6 \ ≤ \ -9 \ + \ 6 \ ⇒ \ x \ ≤ \ -3\)
Now, Since the variable (\(x\)) is lower than or equal to \(-3\), we must find \(-3\) and then draw a close circle above it. Afterward, draw a line to the right.
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Graphing Single Variable Inequalities Quiz