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Chapter 7: Q. 367 (page 732)

In the following exercises, solve each rational inequality and write the solution in interval notation.

1x2-16<0

Short Answer

Expert verified

Solution for rational inequality isx鈭�(-4,4).

Step by step solution

01

Step 1. Given Information

Given that the rational inequality is1x2-16<0.

02

Step 2. Algebraic Expression simplification

Take f(x)=1x2-16

On applying formula and simplifying algebraic function,

f(x)=1(x2-42)(x2-42)=(x+4)(x-4)鈭�(a2-b2)=(a+b)(a-b)f(x)=1(x-4)(x+4)

03

Step 3. Critical points

To find the critical points,

(x-4)=0x=4(x+4)=0x=-4

There is an undefined polynomial function using this critical points. Thus, it will not be taken.

Divide the number line and test the polynomial expression sign in intervals.

In 1x2-16<0ininterval(-4,4)f(x)>0,x鈭�(-4,4)

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