Given: 2(3x+4)=20, prove x=2
In algebraic proof

(

4

+

x

−

3

x

3

)

−

2

=

−

(

3

x

3

−

x

−

2

)

=

−

(

x

−

1

)

(

3

x

2

+

3

x

+

2

)

So

∣

∣

(

4

+

x

−

3

x

3

)

−

2

∣

∣

=

|

x

−

1

|

⋅

∣

∣

3

x

2

+

3

x

+

2

∣

∣

Given

ε

>

0

, let

δ

=

min

{

1

,

ε

20

}

and note that

δ

>

0

If

0

<

|

x

−

1

|

<

1

then

0

<

x

<

2

so that

2

<

(

3

x

2

+

3

x

+

2

)

<

20

and

∣

∣

3

x

2

+

3

x

+

2

∣

∣

<

20

So,

∣

∣

(

4

+

x

−

3

x

3

)

−

2

∣

∣

=

|

x

−

1

|

⋅

∣

∣

3

x

2

+

3

x

+

2

∣

∣

<

|

x

−

1

|

⋅

20

<

ε

20

⋅

20

=

ε

We have shown that for any positive

ε

, there is a positive

δ

such that

If

0

<

|

x

−

1

|

<

1

, then

∣

∣

(

4

+

x

−

3

x

3

)

−

2

∣

∣

<

ε

So, by the definition of limit,  

lim

x

→

1

(

4

+

x

−

3

x

2

)

=

2

Step-by-step explanation:

answer: i cant see the picture

step-by-step explanation:

can u take a better picture

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.