All categories

2 years ago

Solve this equation 8+8x=8

Mathematics

2 answers:

Lynna [10]2 years ago

6 0

Answer: The correct answer is: " x = 0 " .

________

Step-by-step explanation:

Given: " 8 + 8x = 8 " ; Solve for "x" ;

________

Method 1)

________

Subtract "8" from each side of the equation:

________

→ " 8 + 8x − 8 = 8 − 8 " ;

→ On the "left-hand side" of the equation:

Note the following "like terms" :

" +8 − 8 = 0 " ;

→ and we are left with "8x" on the "left-hand side" of the equation.

→ On the "right hand side" of the equation:

The "(8 − 8)" = 0 ;

________

And we are left with:

→ " 8x = 0 " ;

________

Now, divide each side of the equation by "8" ;

to isolate "x" on one side of the equation;

& to solve for "x" :

________

→ 8x / 8 = 0/8 ;

to get:

→ " x = 0 " ;

→ which is the correct answer.

________

Method 2)

________

Given: " 8 + 8x = 8 " ; Solve for "x" ;

________

Subtract "8" from each side of the equation; in the following manner:

________

8 + 8x = 8 ;

- 8 = - 8 ;

_____________

0 + 8x = 0 ;

→ We have: " 0 + 8x = 0 " ;

→ Note: On the "left-hand side" ; we have:

" 0 + 8x " ;

We can simplify this to "8x" ; since the "addition property of zero" states that when "0" is added to any value; the resulting value does not change.

Now, we can bring down the "0" from the "right-hand side" of the equation;

And we can rewrite our equation as:

________

→ " 8x = 0 " ;

Now, divide each side of the equation by "8" ;

to isolate "x" on one side of the equation;

& to solve for "x" :

________

→ 8x / 8 = 0/8 ;

to get:

→ " x = 0 " ;

→ which is the correct answer.

________

Method 3)

________

Given: " 8 + 8x = 8 " ; Solve for "x" ;

________

Divide each side of the equation by "8" ;

________

→ " $\frac{(8 + 8x)}{8} =\frac{8}{8}$ " ;

________

To solve:

________

Note: On the "right-hand side" of the equation:

________

Take note that: " $\frac{8}{8} =$ (8 ÷ 8) = 1 " ;

________

Rewrite the equation as:

________

→ " $\frac{(8 + 8x)}{8} =1$ " ;

________

To solve:

________

Note: " $\frac{x}{y} = z$ " ; ↔ $x = z*y$ ; $(y\neq 0)$ ;

________

→ " $\frac{(8 + 8x)}{8} =1$ " ;

→ From the "left-hand side" of the equation;

Let us simplify:

________

→ " $\frac{(8 + 8x)}{8} = \frac{8}{8} + \frac{8x}{8} = 1 + x$ " ;

Now, bring down the "1" from the "right-hand side" of the equation;

and rewrite the equation:

________

→ " 1 + x = 1 " ;

Now, subtract "1" from each side of the equation;

to isolate "x" on one side of the equation;

& to solve for "x" :

________

" 1 + x − 1 = 1 − 1 " ;

→ On the "left-hand side" of the equation:

Note the following "like terms" :

+1 − 1 = 0 " ;

→ and we are left with "x" on the "left-hand side" of the equation.

→ On the "right hand side" of the equation:

The "(1 − 1)" = 0 ;

→ And we are left with:

→ " x = 0 " ;

→ which is the correct answer!

________

The correct answer is: " x = 0 " .

________

Hope that this answer—and the corresponding explanations—

are helpful !

WIshing you the best!

________

kobusy [5.1K]2 years ago

4 0

Hello!

Answer:

x=0

Step-by-step explanation:

Hope this helps!

You might be interested in

How to convert 5x^2-60x+200 to vertex form?

Rom4ik [11]

Y=a(x-h)^2+k

is what vertex form look like. (h,k) is your vertex so in this problem your vertex would be (60,200)

6 0

3 years ago

Multi answer inequality! Please help and comment only if you know!

bearhunter [10]

Answer:

-8, 0, and -12

Step-by-step explanation:

Using -7 would get you 8. Using -5 would get you 4

6 0

3 years ago

For some integer n, the first, the third and the fifth terms of an arithmetic sequence are respectively 3n, 5n – 6, and 11n + 8.

Mazyrski [523]

Answer:

a₄=8n+1= -39.

Step-by-step explanation:

1) if a₁=3n; a₃=5n-6 and a₅=11n+8, then it is possible to calculate the difference according to 0.5(a₅-a₃)=0.5(a₃-a₁). Then

2) 0.5(11n+8-5n+6)=0.5(5n-6-3n); ⇔ 6n+14=2n-6; ⇔ n= -5.

3) if n=-5, then the 4th term is:

$a_4=\frac{a_5+a_3}{2}; \ = > \ a_4=\frac{11n+8+5n-6}{2}=8n+1;$

or a₄=-39.

8 0

2 years ago

Determine if the given mapping phi is a homomorphism on the given groups. If so, identify its kernel and whether or not the mapp

shtirl [24]

Answer:

(a) No. (b)Yes. (c)Yes. (d)Yes.

Step-by-step explanation:

(a) If $\phi: G \longrightarrow G$ is an homomorphism, then it must hold

that $b^{-1}a^{-1}=(ab)^{-1}=\phi(ab)=\phi(a)\phi(b)=a^{-1}b^{-1}$ ,

but the last statement is true if and only if G is abelian.

(b) Since G is abelian, it holds that

$\phi(a)\phi(b)=a^nb^n=(ab)^{n}=\phi(ab)$

which tells us that $\phi$ is a homorphism. The kernel of $\phi$

is the set of elements g in G such that $g^{n}=1$ . However,

$\phi$ is not necessarily 1-1 or onto, if $G=\mathbb{Z}_6$ and

n=3, we have

$kern(\phi)=\{0,2,4\} \quad \text{and} \quad\\\\Im(\phi)=\{0,3\}$

(c) If $z_1,z_2 \in \mathbb{C}^{\times}$ remeber that

$|z_1 \cdot z_2|=|z_1|\cdot|z_2|$ , which tells us that $\phi$ is a

homomorphism. In this case

$kern(\phi)=\{\quad z\in\mathbb{C} \quad | \quad |z|=1 \}$ , if we write a

complex number as $z=x+iy$ , then $|z|=x^2+y^2$ , which tells

us that $kern(\phi)$ is the unit circle. Moreover, since

$kern(\phi) \neq \{1\}$ the mapping is not 1-1, also if we take a negative

real number, it is not in the image of $\phi$ , which tells us that

$\phi$ is not surjective.

(d) Remember that $e^{ix}=\cos(x)+i\sin(x)$ , using this, it holds that

$\phi(x+y)=e^{i(x+y)}=e^{ix}e^{iy}=\phi(x)\phi(x)$

which tells us that $\phi$ is a homomorphism. By computing we see

that $kern(\phi)=\{2 \pi n| \quad n \in \mathbb{Z} \}$ and

$Im(\phi)$ is the unit circle, hence $\phi$ is neither injective nor

surjective.

7 0

3 years ago

Which is the length of the unknown leg in the right triangle?

Scilla [17]

The answer might be 42.

6 0

3 years ago

Read 2 more answers