# How do you solve and graph the compound inequality #x- 3 > 3# and #-x + 1 < -2# ?

##### 1 Answer

Please read the explanation.

#### Explanation:

We are given the **Compound Inequality**:

We can solve these inequalities separately.

Since **Join** the two inequalities,

the **final result** will be the **intersection** of the two given inequalities.

**Inequality-1**

Add

**...Res.1**

**Inequality-2**

Subtract

Multiply both sides of the inequality by **reverse the inequality**:

**... Res.2**

Using the **intermediate results (Res.1) and (Res.2)**, we get

**FINAL SOLUTION**:

Using **Interval Notation**:

**Important Note:**

**Dotted Lines** in all the graphs below represent a **solution** that does not include a certain value, indicated by the **dotted line**.

**Graph.1**

Graph of the inequality:

**Graph.2**

Graph of the inequality:

**Graph.3: Solution Graph**

**Overlapping area** in the graph is our required solution,

Compare this graph with the following graph.

Both the graphs represent the same solution.

**Graph.4: Solution Graph**

Hope this helps.