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Chapter 9: Q 9.134 (page 974)

Solve 鈭�x2+8x鈭�14<0algebraically. Write the solution in interval notation.

Short Answer

Expert verified

The solution in interval notation is -鈭�鈥�,鈥�-2+4鈭�2+4,鈥�鈭�鈥�.

Step by step solution

01

Step 1. Given information

鈭�x2+8x鈭�14<0

02

Step 2. Solve.

Write the quadratic inequality in standard form.

鈭�x2+8x鈭�14<0

Multiply both sides of the inequality by 鈭�1Remember to reverse the inequality sign.

x2-8x+14>0

Determine the critical points by solving the related quadratic equation.

x2-8x+14=0

Write the quadratic formula

x=-b卤b2-4ac2ax=8卤-82-41路1421x=4卤2x=4+2,orx=4-2

Use the critical points to divide the number line into intervals.

Test numbers from each interval in the original inequality.

03

Step 3. Solution

The solution in interval notation is-鈭�鈥�,鈥�-2+4鈭�2+4,鈥�鈭�鈥�

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