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Chapter 9: Q. 524 (page 987)

In the following exercises, solve each inequality algebraically and write any solution in interval notation:

x2+x>鈥�12

Short Answer

Expert verified

The solution of the inequality is-鈭�鈥�,鈥�-4鈭�3,鈥�鈭�鈥�.

Step by step solution

01

Step 1. Given information. 

We have:

x2+x>鈥�12

02

Step 2. Write the inequality in standard form.

Here, x2+x>鈥�12

Subtract 12from both sides:

x2+x-12>鈥�12-12x2+x-12>鈥�0

03

Step 2. Solve the inequality. 

Change the sign >with =and solve by quadratic formula.

x2+x-鈥�12=0For鈥�a鈥�quadratic鈥�equation鈥�of鈥�the鈥�form鈥�ax2+bx+c=0鈥�the鈥�solutions鈥�are鈥�x1,鈥�2=-b卤b2-4ac2aFor鈥�a=1,鈥�b=1,鈥�c=-12x1,鈥�2=-1卤12-4路鈥�1路-122路鈥�1x1,鈥�2=-1卤鈥�72路鈥�1x=3,鈥�x=-4

Separate into possible cases:

x+4>0x-3>0x+4<0x-3<0x>-4x>3x<-4x<3

Find the intersections:

x鈭�3,+鈭�x鈭�-鈭�,-4

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