All categories

3 years ago

Which of the following equations has the same solution as 3x-5=5x+11?

2 answers:

4 0

3x-5=5x+11

subtract 3x to both sides

3x-5 - 3x =5x+11 - 3x

simplify
-5 = 2x +11

answer is D. -5=2x+11

goldenfox [79]3 years ago

3 0

The equation that matches the same solution as $3x-5=5x+11$ is $\boxed{{\mathbf{Option D}}\to{\mathbf{-5=2x+11}}}$ .

Further explanation:

The expression is given as $3x-5=5x+11$ .

Now, the above expression is simplified as follows:

$\begin{aligned}3x-5x&=11+5\\-2x&=16\\x&=-\frac{{16}}{2}\\x&=-8\\\end{aligned}$

Therefore, the value of $x$ for the given expression is $-8$ .

Now, the four options are given below.

$\begin{gathered}{\text{OPTION A}}\to2x-5=11\hfill\\{\text{OPTION B}}\to3x=5x+6\hfill\\{\text{OPTION C}}\to3x+6=5x\hfill\\{\text{OPTION D}}\to-5=2x+11\hfill\\\end{gathered}$

The simplified form of OPTION A $2x-5=11$ is given below.

$\begin{aligned}2x-5&=11\\2x&=11+6\\2x&=17\\x&=\frac{{17}}{2}\\x&=8.5\\\end{aligned}$

The above solution $x=8.5$ of the expression $2x-5=11$ does not match with the obtained solution $x=-8$ .

Therefore, OPTION A is not the correct answer.

The simplified form of OPTION B $3x=5x+6$ is given below.

$\begin{aligned}3x&=5x+6\\3x-5x&=6\\-2x&=6\\x&=-3\\\end{aligned}$

The above solution $x=-3$ of the expression $3x=5x+6$ does not match with the obtained solution $x=-8$ .

Therefore, OPTION B is not the correct answer.

The simplified form of OPTION C $3x+6=5x$ is given below.

$\begin{aligned}3x+6&=5x\\3x-5x&=-6\\-2x&=-6\\x&=3\\\end{aligned}$

The above solution $x=3$ of the expression $3x+6=5x$ does not match with the obtained solution $x=-8$ .

Therefore, OPTION C is not the correct answer.

The simplified form of OPTION D $-5=2x+11$ is given below.

$\begin{aligned}-5&=2x+11\\-5-11&=2x\\-\frac{{16}}{2}&=x\\x&=-8\\\end{aligned}$

The above solution $x=-8$ of the expression $-5=2x+11$ matches with the obtained solution $x=-8$ .

Therefore, OPTION D is the correct answer.

Thus, the equation that matches the same solution as $3x-5=5x+11$ is $\boxed{{\mathbf{Option D}}\to{\mathbf{-5=2x+11}}}$ .

Learn more:

1. Which expression is equivalent to ? brainly.com/question/3658196

2. What are the values of x? brainly.com/question/2093003

3. Which expression is a sum of cubes? brainly.com/question/4102355

Answer Details:

Grade: Junior High School

Subject: Mathematics

Chapter: Linear equations

Keywords: expression, equivalent, match, options, $3x-5=5x+11$ , $-5x=2x+11$ , equation of line.

You might be interested in

Q: A cell phone company charges $60.00 a month for up to 1 gigabyte of data. The cost of additional data is $0.05 per megabyte.

DiKsa [7]

The linear equation which can be used to determine a user's monthly

bill is c = 60 + 0.05 d ⇒ D

Step-by-step explanation:

The given is:

A cell phone company charges $60.00 a month for up to 1 gigabyte of data
The cost of additional data is $0.05 per megabyte
d represents the number of additional megabytes used
c represents the total charges at the end of the month

We need to find which equation can be used to determine a user's monthly bill

The form of the linear equation is y = mx + b, where b is the constant amount and m is the rate of change

∵ The company charges $60.00 a month for up to 1 gigabyte of data

- That means it is a constant amount each month

∴ b = 60

∵ The cost of additional data is $0.05 per megabyte

- That means it depends on the number of additional megabyte,

so it is not constant, it is the rate of change

∴ m = 0.05

∵ d represents the number of additional megabytes

∴ x = d

∵ c represents the total charges at the end of the month

∴ y = c

Substitute y by c, m by 0.05, x by d and b by 60 in the form of the linear equation above

∴ c = 0.05 d + 60

- We can rearrange the terms of the right hand side

∴ c = 60 + 0.05 d

The linear equation which can be used to determine a user's monthly

bill is c = 60 + 0.05 d

Learn more:

You can learn more about linear function in brainly.com/question/9801816

#LearnwithBrainly

7 0

3 years ago

Translate the phrase, then simplify. Subtract eighty-two from one hundred fifty

emmasim [6.3K]

Answer:

It is 18

Step-by-step explanation:100-82=18

7 0

3 years ago

Look at points C and D on the graph: point C (-2,0), point D (2,4)

Svetach [21]

The answer to the question you are looking for is right in front of u

6 0

3 years ago

18/4(-11.5) Answer that question Thank You!!!

Paha777 [63]

Answer: 207/4 or -51.75

Step-by-step explanation:

3 0

3 years ago

According to a study done by Nick Wilson of Otago University Wellington, the probability a randomly selected individual will not

Lorico [155]

Answer and Step-by-step explanation:

From the question statement we get know that it is Binomial distribution because there are only two possible outcomes so we need to use Binomial Probability Distribution for this question.

Formula for the Binomial Probability Distribution:

P(X)= p^x q^(n-x)

Where,

C_x^n=n!/(n-x)!x! (i.e. combination)
x= total number of successes
p=probability of success (p=1-q)
q=probability of failure (q=1-p)
n=number of trials
P(X)= probability of total number of successes

Answer and explanation for each part of the question are as follow:

a.What is the probability that among 10 randomly observed individuals exactly 4 do not cover their mouth when sneezing?

Solution:

Given that

n=10

p=0.267 (because p is the probability of success which is “number of individuals not covering their mouths when sneezing” in the question)

q=1-0.267=0.733

x=4 (number of successes i.e. individuals not covering their mouths)

C_x^n=n!/(n-x)!x!=10!/(10-4)!4!=210

P(X)=C_x^n p^x q^(n-x)=210×〖(0.267)〗^4×〖0.733〗^(10-4)

P(X)=210×0.00508×0.155

P(X)=0.165465

b. What is the probability that among 10 randomly observed individuals fewer than 3 do not cover their mouth when sneezing?

Solution:

Given that

n=10

p=0.267 (because p is the probability of success which is “number of individuals not covering their mouths when sneezing” in the question)

q=1-0.267=0.733

x=3 (number of successes i.e. individuals not covering their mouths)

C_x^n=n!/(n-x)!x!=10!/(10-3)!3!=120

P(X)=C_x^n p^x q^(n-x)=120×(0.267)^3×〖0.733〗^(10-3)

P(X)=120×0.01903×0.1136

P(X)=0.25962

c. Would you be surprised if, after observing 18 individuals, fewer than half covered their mouth when sneezing? why?

Solution:

Given that

n=18

p=0.267 (because p is the probability of success which is “number of individuals not covering their mouths when sneezing” in the question)

q=1-0.267=0.733

x=9 (x is the number of successes “number of individuals not covering their mouths when sneezing”, if less than half cover their mouth then more than half will not cover), so let x=9

C_x^n=n!/(n-x)!x!=18!/(18-9)!9!=48620

P(X)=48620×(0.267)^9×〖0.733〗^(18-9)

P(X)=48620×0.00000689×0.0610

P(X)=0.020

Yes, I am surprised that probability of less than 9 individuals covering their mouth when sneezing is 0.020. Which is extremely is small.

3 0

3 years ago