## 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**.

**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**.

### 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 \(x \ > \ -2\)

**greater**than \(3\), first, we should find \(3\), then draw an

**open circle**above it and draw a line to the

**right**.

**2)** Make a graph for \(x \ ≤ \ 1\)

**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**.

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

**isolate**the variable. To do this

**subtract**\(3\) from both sides:

\(x \ + \ 3 \ - \ 3 \ ≥ \ -2 \ - \ 3 \ ⇒ \ x \ ≥ \ -5\)

**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**.

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

**isolate**the variable. To do this

**add**\(9\) to both sides:

\(x \ - \ 9 \ + \ 9 \ ≤ \ -10 \ + \ 9 \ ⇒ \ x \ ≤ \ -1\)

**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**.

**5)** Make a graph for \(x \ > \ -4\)

**greater**than \(-4\), first, we should find \(-4\), then draw an

**open circle**above it and draw a line to the

**right**.

**6)** Make a graph for \(x \ < \ 5\)

**lower**than \(5\), you must find \(5\) and then draw an

**open circle**above it. Afterward, draw a line to the

**left**.

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

**isolate**the variable. To do this

**add**\(6\) to both sides:

\(x \ - \ 6 \ + \ 6 \ < \ -3 \ + \ 6 \ ⇒ \ x \ < \ 3\)

**lower**than \(3\), we must find \(3\) and then draw an

**open circle**above it. Afterward, draw a line to the

**left**.

**8**

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

**isolate**the variable. To do this

**add**\(7\) to both sides:

\(x \ - \ 7 \ + \ 7 \ < \ -5 \ + \ 7 \ ⇒ \ x \ < \ 2\)

**lower**than \(2\), we must find \(2\) and then draw an

**open circle**above it. Afterward, draw a line to the

**left**.

**9**

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

**isolate**the variable. To do this

**subtract**\(11\) from both sides:

\(x \ + \ 11 \ - \ 11 \ > \ 13 \ - \ 11 \ ⇒ \ x \ > \ 2\)

**greater**than \(2\), we must find \(2\) and then draw an

**open circle**above it. Afterward, draw a line to the

**right**.

**10**

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

**isolate**the variable. To do this

**add**\(6\) to both sides:

\(x \ - \ 6 \ + \ 6 \ ≤ \ -9 \ + \ 6 \ ⇒ \ x \ ≤ \ -3\)

**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**.