**Solve inequalities :**

An open sentence that contains the symbol <, >, ≤ or ≥ is called an inequality. Inequalities can be solved in the same way as equations.

## Equation |
## Inequality | |

In equation, we will have = (equal) sign. |
In equation, we will have one of the following signs <, >, ≤ or ≥ | |

By solving the equation, we will get only one value as the solution. |
By solving given inequality, we will get more than one solution that satisfies the given condition. |

**Example 1 :**

Solve each inequality. Then check your solution, and graph it on a number line.

x + 14 ≥ 18

**Solution : **

**Step 1 :**

x + 14 ≥ 18

Subtract 14 on both sides,

x + 14 - 14 ≥ 18 - 14

x ≥ 4

**Step 2 :**

To check the solution, we need to take any values greater than or equal to 4 and check whether it satisfies the condition or not.

Let us take x = 5

Now we have to apply 5 instead of "x" in the given inequality.

5 + 14 ≥ 18

19 ≥ 18 (True)

**Step 3 :**

To graph the solution, we have to draw a number line and shade the portion which satisfies the given condition.

**Example 2 :**

Solve each inequality. Then check your solution, and graph it on a number line.

d + 5 ≤ 7

**Solution : **

**Step 1 :**

d + 5 ≤ 7

Subtract 5 on both sides,

d + 5 - 5 ≤ 7 - 5

d ≤ 2

**Step 2 :**

To check the solution, we need to take any value less than or equal to 2 and check whether it satisfies the condition or not.

Let us take d = 0

Now we have to apply 0 instead of "d" in the given inequality.

0 + 5 ≤ 7

5 ≤ 7 (True)

**Step 3 :**

To graph the solution, we have to draw a number line and shade the portion which satisfies the given condition.

**Example 3 :**

Solve each inequality. Then check your solution, and graph it on a number line.

-3 ≥ q - 7

**Solution : **

**Step 1 :**

-3 ≥ q - 7

Add 7 on both sides

-3 + 7 ≥ q - 7 + 7

7 ≥ q

If we flip the variable to the right side and value to the left side, then we have to change its original sign.

q ≤ 7

**Step 2 :**

To check the solution, we need to take any value lesser than or equal to 7 and check whether it satisfies the condition or not.

Let us take q = 5

Now we have to apply 5 instead of "q" in the given inequality.

-3 ≥ 5 - 7

-3 ≥ - 2 (True)

**Step 3 :**

To graph the solution, we have to draw a number line and shade the portion which satisfies the given condition.

**Example 4 :**

Solve each inequality. Then check your solution, and graph it on a number line.

2y > -8 + y

**Solution : **

**Step 1 :**

2y > -8 + y

Subtract y on both sides

2y - y > -8 + y - y

y > -8

**Step 2 :**

To check the solution, we need to take any value greater than -8.

Let us take y = -5

Now we have to apply -5 instead of "y" in the given inequality.

2(-5) > -8 - 5

-10 > -13 (True)

**Step 3 :**

**Example 5 :**

Solve each inequality. Then check your solution, and graph it on a number line.

3f < -3 + 2f

**Solution : **

**Step 1 :**

3f < -3 + 2f

Subtract 2f on both sides

3f - 2f < -3 + 2f - 2f

f < -3

**Step 2 :**

To check the solution, we need to take any value lesser than -2.

Let us take f = -2

Now we have to apply -2 instead of "f" in the given inequality.

3(-2) < -3 + 2(-2)

-6 < -3 - 4

-6 < -7 (True)

**Step 3 :**

After having gone through the stuff given above, we hope that the students would have understood "Solve inequalities".

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