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Chapter 4: Q. 41 (page 246)

Solve each inequality. Graph the solution set.

x3+x2<4x+4

Short Answer

Expert verified

The real zeroes are -1,2,-2and the solution set can be graphed as

Step by step solution

01

Step 1. Given Information

The given inequality isx3+x2<4x+4

02

Step 2. Calculation

Solve the given inequality as follows,

x3+x2-4x-4<4x+4-4x-4x3+x2-4x-4<0x3+x2-4x-4=0x2(x+1)-4(x+1)=0(x+1)(x2-4)=0x+1=0鈬�x=-1x2-4=0鈬�x=卤2

Thus, the real zeroes of function are-1,2and-2

03

Step 3. Graph

Construct the table by using a number from each interval to check whether the function is positive or negative.

Thus, the solution set is (-鈭�,-2)鈭�(-1,2)

And the solution set can be graphed as

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