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Chapter 2: Q321. (page 184)

Solve the equality, graph the solution on the number line and express the solution in the interval notation.

6n-123-n鈮�9n-4+9n

Short Answer

Expert verified

Indentity

-鈭�,鈭�

Step by step solution

01

Step 1. Given information.

The given inequality is

6n-123-n鈮�9n-4+9n

02

Step 2. Solving the inequality.

Distributing and combining like terms:

6n-36+12n鈮�9n-36+9n=>18n-36鈮�18n-36

Subtracting both sides by 18n-36:

18n-36-19n-36鈮�18n-36-18n-36

Simplifying

0鈮�0

Since the variables (n) are gone and we have a true statement, the inequality is an identity and the solution is all real numbers.

03

Step 3. Graphing the solution on the number line.

The graph of the solution on the number line is presented below:

04

Step 4.  Writing the solution in the interval notation.

In the interval notation, the solution can be expressed as

-鈭�,鈭�

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