1 2 x + 3

Solve inequalities is no different than solving regular
equations.  In both cases, you need to get all the x terms on one side of the equation
and all the numbers on the other.

One way to do this
question is this:

Subtract 4x from both sides.  You now
have

-3.5x + 3 <
-7

Subtract 3 from both
sides

-3.5x <
-10

Divide both sides by -3.5.  Be sure to switch the
direction of the inequality sign.

x >
2.85

If you prefer, you can multiply both sides by 2 to get
your .5x to be x.

x + 6 < 8x -
14

Then you move the 8x and the
6.

-7x < -20

Again, be
sure to switch the direction of the inequality sign.

x
> 20/7

or

x >
2.85

Solve using the quadratic formula: 3x^2 -5x -4 = 0

The roots x1 and x2 of the quadratic equation ax^2+bx+c =
0 is given by the formula:

x1 = {-b+sqrt(b^2-4ac)}/2
and

x2 =
-{b+sqrt(b^2-4ac)}/2.

The given quadratic equation is
3x^2-5x-4 = 0.

So a = 3, b= -5 and c=
-4.

So using the formula we get the two
roots:

x1 = {-(-5)+sqrt(-5)^2-4*3(-4)}/2*3 =
{5+sqrt(25+48)}/6

x1 =
{5+sqrt(73)}/6.

x2 =
{5-sqrt(73)}/6.

Show how "The Flea" is a metaphysical poem by John Donne?

Metaphysical poetry involves the elevation of a seemingly
common item or action to an almost spiritual level of importance, and John Donne’s “The
Flea” illustrates this definition perfectly.

In
the poem, the speaker equates the “two bloods mingled” within the body of a flea with
the marriage of a man and his wife. Thus, the speaker argues to his lover that they,
from a certain perspective, are “one blood made of two.” From the speaker’s perspective,
the engorged flea is elevated from a pest to a “marriage bed” and “marriage temple.” The
speaker seemingly transfers the sacred characteristics, meanings, and implications of
marriage to a common flea.

However, the speaker
does not stop with this argument. To reinforce his point, the speaker also warns his
lover to not kill the flea because to do so would be “self murder.” By killing the flea,
one would be destroying a part of the speaker and his lover as well as their “union.”
 Thus, the value of the flea is elevated to that of a human life as well.

How would you explain the change in relationship between Gregor and his family thanks to his transformation in "The Metamorphosis"?

Your original question did not really make much sense, so
I have edited it to make it hopefully more understandable, both to you and to me. Well,
it is quite clear that Gregor's transformation has wrought significant changes in his
relations with his family. Although his sister at first tries to show love and kindness
to Gregor, finding him food that he will eat, she later regards him with hatred. It is
she that confronts the facts and also forces her parents to confront them as well when
she says:

"My
dear parents... things cannot go on like this. You may not realise it, but I do. I will
not pronounce my brother's name in front of this monstrosity, and so all I will say is:
We must try to get rid of it. We have done everything humanly possible to look after it
and put up with it; I do not believe there is anything we can be reproached
for."

This, of course, is the
ultimate betrayal that arguably is responsible for Gregor's death as he faces the way
that even the most seemingly stable and solid affections have turned against him thanks
to his transformation.

Of course, although it is his mother
who is dragged along by the will of the others, his father, from the first day, makes
his animosity known towards his son. Note how he tries to crush Gregor. Gregor reflects
on the size of his father's boot soles, but not for
long:

But he
did not dwell on this; after all, from the very first day of his new life, he had known
that the father viewed only the utmost severity as appropriate for dealing with
him.

Above all, the change in
relationship is characterised by the way in which the family celebrate and are happy
when Gregor finally dies and leaves them to focus on the future and live a happy
life.

Solve for x: lg(8x+9) + lgx = 1 + lg(x^2 - 1)

Given the logarithm
equation:

lg (8x+9) + lg (x) = 1+ lg
(x^2-1)

We need to find x
value.

We will use logarithm properties to
solve.

First, we know that lg a + lg b = lg
(ab)

==> lg (x(8x+9) = 1 + lg (x^2
-1)

Also, we know that lg 10 =
1

==> lg (8x^2 + 9x) = lg 10 + lg
(x^2-1)

==> lg (8x^2 +9x) = lg
10(x^2-1)

==> lg (8x^2 +9x) = lg (10x^2
-10)

Now we have the logs are equal, then the bases are
equal too.

==> 8x^2 + 9x = 10x^2 -
10

We will combine like
terms.

==> 2x^2 - 9x -10 =
0

Now we will find the
roots.

==> x1= ( 9 + sqrt(81+80) / 4 = (9+sqrt(161)
/ 4

==> x2= (9-sqrt(161) / 4 ( Not
valid)

Then, the answer
is:

x = (9 + sqrt161)
/4

How is Romeo presented to the audience in Romeo and Juliet?Comment on the language used about him and by him.

I think that a clear case can be made to reflect that
Romeo is depicted as a character of pure emotion.  There is an affectual side to Romeo
that is quite evident even in the earliest phases of the play.  When Lord Montague
describes him as "his own affections' counselor," it highlights the strong sense of
emotional affect that is within him.  We see this throughout the play.  At the outset of
the play, there is a melancholy that impacts Romeo.  There is not a clear reason as to
why he feels what he feels, but it is evident that he "feels" and this helps to
establish a baseline for the character that is fairly constant throughout the drama. 
His infatuation for Rosaline, the immediacy in which he is enamored with Juliet, his
intensity regarding the killing of Tybalt, and the strict desire to escape with Juliet,
all reflect an emotional intensity that is inherent in his character.  In the couple, it
seems as if Romeo is the heart while Juliet is the "brains" of the operation.  Romeo is
shown to be extremely emotional and lacking moderation in feeling and displaying these
emotions.

Closely analyzing Edmund's "Thou, nature, art my goddess" speech in King Lear, explain what Edmund says and what it shows about his character.In...

In act one, scene 2 of King Lear
(lines 1-23), Edmund reconfirms his life's creed and its
goals.

"Thou, nature, art my
goddess":  You, nature (natural selection, survival of the fittest, etc.) are
my inspiration and leader.

"To thy law my
services are bound":  I am not bound by society's laws but by the laws of
nature, (the law of the jungle).

"Wherefore
should I stand in the plague of custom":  Why should I be constrained by the
limitations of society...

"and permit the
curiosity of nations to deprive me":  and allow its particular and arbitrary
rules to hold me back...

"for that I am some
twelve or fourteen moonshines lag of a brother?":  just because I'm 12 or 14
months younger than my brother?

"Why 'bastard'? 
Wherefore 'base'?":  Why am I called a 'bastard' (illegitimate)? Why am I
considered 'inferior'?...

"When my dimensions are
as well compact":  considering that my body is as
strong...

"my mind as generous and my shape as
true as honest madam's issue?":  my mind is as capable, and my looks are as
good as those of a child of some respectable woman? (as opposed to that of a whore, like
my mother).

"Why brand they us with 'base,' with
'baseness,' 'bastardy,' 'base,' 'base'?":  Why do they stamp
us with terms like 'inferior,' 'inferiority,
'illegitimate,' 'inferior,' 'inferior'?...

"who,
in the lusty stealth of nature, take more composition and fierce quality than doth
within a dull, stale, tired bed go to the creating a whole tribe of fops got 'tween
asleep and wake?":  us who, conceived in hot and
hidden sexual passion, are created with more substance and strength than are a whole
tribe of weaklings made by two people in bed who are half
asleep?!

"Well then, legitimate Edgar, I must
have your land.":  Well then, my 'valid' brother Edgar - because you are one
of those weaklings (created in the way I've described above), it is only fitting that I,
the stronger and fitter brother, should have what is now considered
yours.

"Our father's love is to the bastard
Edmund as to th' legitimate":  After all, our father loves me, the 'bastard,'
as much as he loves you, the 'valid' one.

"Fine
word, 'legitimate'":  Fine word,
'valid.'

"Well, my legitimate, if this letter
speed and my invention thrive, Edmund the base shall top th' legitimate.": 
Well, my valid one, if this letter (the fake one I've devised by forging your
handwriting) works and my plan succeeds, I (the inferior one) will vanquish the
'valid.'

"I grow, I prosper.":  I get
stronger, I thrive.

"Now, gods, stand up for
bastards!":  Now, you, the powers-that-be, stand up for us
'bastards''!

Edmund, the son of a whore -- slighted,
neglected and derided from birth -- has become as hard and tough in his heart and mind
as he has in his body.  As the play will show, he will do whatever it takes (deceive,
betray, kill) to get what he feels is rightfully his.