Question

Solve the inequality and express your answer in interval notation. X^2-6x+7<0

Answer 1

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)