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

tearstreakdl
2021-12-15
Answered

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

You can still ask an expert for help

Elaine Verrett

Answered 2021-12-16
Author has **41** answers

Explanation:

First, factorise the x terms.

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

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

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$\left(<0\right)$ . 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${x}^{2}-6x-7>0$ , the portions of the curve that are positive is when $x<-1$ and $x>7$ )

First, factorise the x terms.

To find the roots:

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

Do a rough sketch of a graph showing

- 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

This means the curve is negative between

Which is expressed as

(If the question states

Jenny Bolton

Answered 2021-12-17
Author has **32** answers

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

$x<-1,\text{}-1x7,\text{}x7$

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

find the zeros

These indicate where the function changes sign

the zeros split the x-axis into 3 intervals

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

asked 2021-10-15

To calculate: Whether the point (-5, 2) lies in the region for the graph of the system of inequalities $x+2y<3\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}-4x+y2$ or not,

asked 2022-02-05

If $a=4,b=8,\text{and}\text{}c=5$ , what is $c\cdot \frac{bc}{4}-(7-a)$ ?

asked 2021-09-26

The mean distance of Earth from the Sun is $9.29\times 1079.29\times {10}^{7}$ miles. The orbit of Earth around the Sun is circular and that 1 revolution takes 365 days; find the linear speed of Earth.

asked 2022-02-04

What is x if $3x+5=32?$

asked 2021-12-04

Which expression is equivalent to 5i?

A.$\sqrt{-5}$

B.$-\sqrt{5}$

C.$\sqrt{-25}$

D.$-\sqrt{25}$

A.

B.

C.

D.

asked 2022-02-06

How do you simplify $24b-b$ ?

asked 2022-02-04

How do you simplify $-3\{4x-2[3x-4(x-1)-2]-3\}+7$ ?