Step-by-step explanation:
Notation x^2-6x-7<0
x2−6x−7<0
Convert the inequality to an equation.
x2−6x−7=0
Factor
x2−6x−7
using the AC method.
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(x−7)(x+1)=0
Set
x−7=0
and solve for x.
Set the factor equal to 0.
x−7=0
Add
7
to both sides of the equation.
x=7
Set
x+1=0
and solve for x.
x=−1
Consolidate the solutions.
x=7,−1
Use each root to create test intervals.
x<−1−1<x<7x>7
Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.
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x<−1
False
−1<x<7
True
x>7
False
The solution consists of all of the true intervals.
−1<x<7
Convert the inequality to interval notation.
(−1,7)
