**Graph a linear inequality in one variable : **

To graph a linear inequality in one variable, first we have to draw a number line.

Now we have to draw a arrow to represent the given inequality.

For example x < 5 means the value of the variable x is lesser than 5. So it may be 4, 3, 2, 1, 0. We have to graph the given linear inequality as follows.

- Whenever we have the symbol " < " or " > " inequality in the given question, we have to use open circle.
- Whenever we have the symbol " ≤ " or " ≥ " inequality in the given question, we have to use closed circle.

**Example 1 :**

Graph the solutions of the inequality x ≥ -2. Check the solutions.

**Solution : **

**Step 1 :**

Draw a closed circle at -2 to show that -3 is a solution.

**Step 2 :**

Shade the number line to the right of -2 to show that numbers greater than -2 are solutions.

(Use a solid circle for an inequality that uses ≥ or ≤)

**Step 3 :**

Check your solution.

Choose a number that is on the shaded section of the number line, such as -1.

Substitute -1 for x.

-1 ≥ -2

-1 is greater than -2, so -1 is a solution.

**Step 4 :**

Let us prove that -2 is a solution of the inequality x ≥ -2.

In the given inequality, plug y = -2.

Then, we have

-2 ≤ -2 ---> (-2 is greater than or equal to -2) ?

Is the answer for the above question is "yes or "no" ?

The answer for the above question is "Yes".

Because, -2 is equal to -2.

Hence, -2 is a solution to the inequality x ≥ -2.

**Example 2 :**

Graph the solutions of the inequality x ≥ 6. Check the solutions.

**Solution : **

**Step 1 :**

Draw a closed circle at 6 to show that 6 is a solution.

**Step 2 :**

Shade the number line to the right of 6 to show that numbers greater than 6 are solutions.

(Use a solid circle for an inequality that uses ≥ or ≤)

**Step 3 :**

Check your solution.

Choose a number that is on the shaded section of the number line, such as 7.

Substitute 7 for x.

7 ≥ 6

7 is greater than 6, so 6 is a solution.

**Step 4 :**

Let us prove that 6 is a solution of the inequality x ≥ 6.

In the given inequality, plug y = 6.

Then, we have

6 ≤ 6 ---> (6 is greater than or equal to 6) ?

Is the answer for the above question is "yes or "no" ?

The answer for the above question is "Yes".

Because, 6 is equal to 6.

Hence, 6 is a solution to the inequality x ≥ 6.

**Example 3 :**

Graph the solutions of the inequality 1 < m. Check the solutions.

**Solution : **

**Step 1 :**

Draw an empty circle at 1 to show that 1 is not a solution.

**Step 2 :**

Shade the number line to the right of 1 to show that numbers greater than 1 are solutions.

(Use an open circle for an inequality that uses > or <)

**Step 3 :**

Check your solution.

Choose a number that is on the shaded section of the number line, such as 2.

Substitute -4 for y.

1 < 2

1 is less than 2, so 2 is a solution.

**Step 4 :**

Let us prove that 1 is not a solution of the inequality 1 < m.

In the given inequality, plug m = 1.

Then, we have

1 < 1 ---> (1 is less than 1) ?

Is the answer for the above question is "yes or "no" ?

The answer for the above question is "No".

Because, 1 is equal to 1.

Hence, 1 is not a solution to the inequality 1 < m.

**Example 4 :**

Graph the solutions of the inequality t ≤ -4. Check the solutions.

**Solution : **

**Step 1 :**

Draw a solid circle at -4 to show that -4 is a solution.

**Step 2 :**

Shade the number line to the left of -4 to show that numbers less than -4 are solutions.

(Use a solid circle for an inequality that uses ≥ or ≤)

**Step 3 :**

Check your solution.

Choose a number that is on the shaded section of the number line, such as -5.

Substitute -5 for t.

-5 ≤ -4

-5 is less than -4, so -5 is a solution.

**Step 4 :**

Let us prove that -4 is a solution of the inequality t ≤ -4.

In the given inequality, plug t = -4.

Then, we have

-4 ≤ -4 ---> (-4 is less than or equal to -4) ?

Is the answer for the above question is "yes or "no" ?

The answer for the above question is "Yes".

Because, -4 is equal to -4.

Hence, -4 is a solution to the inequality t ≤ -4.

After having gone through the stuff given above, we hope that the students would have understood "Graph a linear inequality in one variable".

Apart from the stuff given above, if you want to know more about "Graph a linear inequality in one variable", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**