1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Inessa [10]
3 years ago
7

Use properties to rewrite the given equation. Which equations have the same solution as 3/5x +2/3 + x = 1/2– 1/5x? Check all tha

t apply.
a. 8/5x+2/3=1/2-1/5x
b. 18x + 20 + 30x = 15 – 6x
c. 18x + 20 + x = 15 – 6x
d. 24x + 30x = –5
e. 12x + 30x = –5
Mathematics
2 answers:
VMariaS [17]3 years ago
5 0

Answer:

Only options a ,b,d have the same solution as \frac{3}{5}x +\frac{2}{3}+x=\frac{1}{2}-\frac{1}{5}x

Step-by-step explanation:

Given:

An equation:  \frac{3}{5}x +\frac{2}{3}+x=\frac{1}{2}-\frac{1}{5}x    ....[1]

Like terms states that contain the same variables raised to the same power.

Combine like terms on left hand side in equation [1] we get,

\frac{3}{5}x+x +\frac{2}{3}=\frac{1}{2}-\frac{1}{5}x

\frac{8}{5}x +\frac{2}{3}=\frac{1}{2}-\frac{1}{5}x

we get option (a) as the same solution.

Using LCM(Least Common ) to change each fraction to make their denominators the same as the least common denominator

Taking LCM both sides in Equation (1) ,

\frac{3}{5}x +\frac{2}{3}+x=\frac{1}{2}-\frac{1}{5}x

As LCM(3,5)=15 and LCM(2,5)=10 we have,

\frac{9x+10+15x}{15}= \frac{5-2x}{10}

On simplifying we get,

10(9x+10+15x)= 15(5-2x)=

Dividing both sides by 5 we get,

\frac{10(9x+10+15x)}{5} =\frac{15(5-2x)}{5}

On simplify:

2(9x+10+15x)=3(5-2x)

∴ 18x+20+30x=15-6x

which is same solution as given in option (b).

Now,

Use Additive Property of Equality states that allows one to add the same quantity to both sides of an equation.

Further, using the above property add 6x both sides  in  18x+20+30x=15-6x we get,

18x+20+30x+6x=15-6x+6x

On simplifying we get,

18x+20+30x+6x=15

Subtract 20 from both the sides we get,

18x+20+30x+6x-20=15-20

Simplify:

18x+30x+6x=-5

or, 24x+30x=-5 which is same solution  as given in option(d)

But, options c and e equation doesn't have same solution as \frac{3}{5}x +\frac{2}{3}+x=\frac{1}{2}-\frac{1}{5}x










lorasvet [3.4K]3 years ago
3 0

Answer:

a,b,d

Step-by-step explanation:

You might be interested in
Find the product.<br> 2.05x0.47 =
pshichka [43]

Answer:

0.9625

Step-by-step explanation:

6 0
3 years ago
PLEASEEEE HELP I WILL GIVE BRAINLIEST!!
I am Lyosha [343]

Answer:

The average is 5.41666667 degrees.

Step-by-step explanation:

3 0
3 years ago
Which transformation is a dilation?
dem82 [27]
B. represents a dialation
5 0
3 years ago
A line has a y-intercept of -2, but has no x-intercept. Describe
frutty [35]
If it has no x-intercept, it is a horizontal line going through 0,-2. hope this helps
6 0
3 years ago
Read 2 more answers
There are 500 toothpicks in a small box. If a jumbo box is made by doubling all the dimensions of the small box, how many toothp
Kisachek [45]
Volume is length x width x height. if you double those it is 2length x 2width x 2 height so you are increasing the volume by 8 times (2x2x2). 8 x 500 = 4000<span>                                   D.) 4,000 Toothpicks
</span>
4 0
3 years ago
Read 2 more answers
Other questions:
  • Need Answered ASAP
    8·1 answer
  • In the computer langauge Binary, what "language" can a computer understand?
    13·1 answer
  • The function g is defined by g(x) = 1/2x - 1. What is<br> the value of g(6) ?
    6·1 answer
  • Yvonne made the two-way table below showing students’ favorite fruits.
    8·2 answers
  • 8 1/4 hours of work for a total pay of $99.00 What is the unit rate :)
    14·2 answers
  • What is the area of yhe following circle?either an exact answer in terms of or use 3.14 for and enter your ansert as a decimal
    15·1 answer
  • Please help me ......
    10·1 answer
  • Can Yall answer this for me heart eyes
    11·2 answers
  • In your job with the heating contractor you photograph houses with infrared film and use the pictures to determine where to plac
    12·1 answer
  • The amount of soda a dispensing machine pours into a 12 ounce can of soda follows a normal distribution with a mean of 12.48 oun
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!