How do you solve the inequality x2−6x−7&lt;0

Question

How do you solve the inequality x2−6x−7&amp;lt;0

Elaine Verrett · Accepted Answer

Explanation:
First, factorise the x terms.

x^{2} - 6 x - 7 < 0

(x - 7) (x + 1) < 0

To find the roots:

x - 7 = 0

or

x + 1 = 0

x = 7

or

x = - 1

The question asks us to find the portion of the curve which is less than zero

(< 0)

. Thus, we need to show by giving a range of values of x.
Do a rough sketch of a graph showing

x^{2}

curve on x and y axis
- curve must be positive, meaning it has a minimum point. (like a smile)
- label the x-intercepts with the values found above.
Since the equality given is "<", draw a small circle at the intercepts.
The portion of the curve that is negative falls below

y = 0

This means the curve is negative between

x = - 1

and

x = 7

Which is expressed as

- 1 < x < 7

(If the question states

x^{2} - 6 x - 7 > 0

, the portions of the curve that are positive is when

x < - 1

and

x > 7

)

Jenny Bolton · Accepted Answer

Explanation the quadratic on the left side

\Rightarrow (x - 7) (x + 1) < 0

find the zeros

x = - 1

and

x = 7

These indicate where the function changes sign
the zeros split the x-axis into 3 intervals

x < - 1, - 1 < x < 7, x > 7

Consider a test point in each interval
we want to find where the function is negative, <0
substitute each tst point into the function and consider its

How do you solve the inequality x^2-6x-7<0

Answered question

Answer & Explanation

New Questions in Pre-Algebra