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Chapter 7: Q.497. (page 742)

Solve the rational inequality and write the solution in interval notation.

12+12x2鈮�5x

Short Answer

Expert verified

The solution is-鈭�,0鈭�(0,4]鈭�[6,鈭�).

Step by step solution

01

Step 1. Given information.

The given rational inequality is12+12x2鈮�5x.

02

Step 2. Simplify the inequality.

Solve the given inequality.

12+12x2鈮�5xx2+242x2鈮�5xx2+24鈮�10x2xx2+24鈮�10xx2-10x+24鈮�0x2-6x-4x+24鈮�0xx-6-4x-6鈮�0x-6x-4鈮�0
03

Step 3. Simplified answer.

x-6鈮�0x鈮�6or x-4鈮�0x鈮�4

The domain of the given inequality is -鈭�,0鈭�0,鈭�.

So, the required interval is:

-鈭�,0鈭�(0,4]鈭�[6,鈭�)

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