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WITCHER [35]
3 years ago
7

Solve each proportion. 8/x+9=2/x-3 Please show work.

Mathematics
2 answers:
emmainna [20.7K]3 years ago
7 0


8/x+9-(2/x-3)=0

Step by step solution :


Step 1 :

2
Simplify —
x
Equation at the end of step 1 :

8 2
(— + 9) - (— - 3) = 0
x x
Step 2 :

Rewriting the whole as an Equivalent Fraction :

2.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using x as the denominator :

3 3 • x
3 = — = —————
1 x
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

2 - (3 • x) 2 - 3x
——————————— = ——————
x x
Equation at the end of step 2 :

8 (2 - 3x)
(— + 9) - ———————— = 0
x x
Step 3 :

8
Simplify —
x
Equation at the end of step 3 :

8 (2 - 3x)
(— + 9) - ———————— = 0
x x
Step 4 :

Rewriting the whole as an Equivalent Fraction :

4.1 Adding a whole to a fraction

Rewrite the whole as a fraction using x as the denominator :

9 9 • x
9 = — = —————
1 x
Adding fractions that have a common denominator :

4.2 Adding up the two equivalent fractions

8 + 9 • x 9x + 8
————————— = ——————
x x
Equation at the end of step 4 :

(9x + 8) (2 - 3x)
———————— - ———————— = 0
x x
Step 5 :

Adding fractions which have a common denominator :

5.1 Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

(9x+8) - ((2-3x)) 12x + 6
————————————————— = ———————
x x
Step 6 :

Pulling out like terms :

6.1 Pull out like factors :

12x + 6 = 6 • (2x + 1)

Equation at the end of step 6 :

6 • (2x + 1)
———————————— = 0
x
Step 7 :

When a fraction equals zero :

7.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

6•(2x+1)
———————— • x = 0 • x
x
Now, on the left hand side, the x cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
6 • (2x+1) = 0

Equations which are never true :

7.2 Solve : 6 = 0

This equation has no solution.
A a non-zero constant never equals zero.
Vikki [24]3 years ago
6 0

Answer:

x=7

Step-by-step explanation:

8/x+9 = 2/x-3

(8) x-3 = (2) x+9

8x-24 = 2x+18

6x-24=18

6x=42

x=7

You might be interested in
What is 19.6 divided by 7
Lemur [1.5K]
19 divided by 7 = 2.8
7 0
3 years ago
23. The letters of the alphabet are written on
Alla [95]

Answer:

21/676

Step-by-step explanation:

The total number of letters of the alphabet will be the total outcome which is 26 alphabets.

If consonant numbers are drawn out, the probability of drawing a consonant will be total consonants/total alphabets

Total consonants in the alphabet is 21.

Probability of drawing consonants = 21/26.

Since all the consonants are replaced before drawing a Z, our total outcome will not change i.e it will still be 26.

Probability of drawing a letter Z will be 1/26.

Therefore, the probability of drawing a consonant,replacing it, and then drawing a Z will be;

21/26×1/26

= 21/676

5 0
3 years ago
A company is designing a new cylindrical water bottle. The volume of the bottle will be 211 cm^3. The height of the water bottle
Zinaida [17]

Answer:

The correct answer is 2.912 cm.

Step-by-step explanation:

A company is designing a new cylindrical water bottle.

Volume of a cylinder is given by π × r^{2} × h, where h is the height of the cylinder and r is the radius of the cylinder.

The volume of each bottle will be 211 cm^{3}.

The height (h) of the water bottle be 7.9 cm.

Let the radius of the bottle be r cm.

∴ π × r^{2} × h = 211 ; (π = 3.15)

⇒ r^{2} × 24.885 = 211

⇒ r = 2.912

The radius of the water bottle is 2.912 cm.

4 0
3 years ago
1. 2x + 4 = 3(x – 2) + 1
sweet [91]
Please, do not post more than 1 or 2 questions at a time.  Out of courtesy I will address one of your six questions here:

<span>2x + 4 = 3(x – 2) + 1

You are to solve this for x.

1) perform the multiplication:     </span><span>2x + 4 = 3x - 6 + 1
2) combine like terms:                4+6-1 = x
3) solve for x:                              x = 11
4) check:  Is 2(11) + 4 = 3(11-2) + 1 true?
   Is 22+4 = 33-6 true?  NO.  Try again, looking for the mistake:

</span><span>2x + 4 = 3(x – 2) + 1  =>   2x + 4 = 3x - 6 + 1
                                                  4 = x - 5
                                                  9 = x

Check:  Is 2(9) + 4 = 3(9-2) + 1 true?  Is 18+4 = 22 true?  YES.
The solution to #1 is  x = 9  (answer).

Submit your other questions separately, please.

</span>
8 0
3 years ago
When building a house, the number of days required to build varies inversely with with the number of workers. One house was buil
Helga [31]

Let d represent number of days and n represent number of workers.

We have been given that when building a house, the number of days required to build varies inversely with with the number of workers.

We know that the equation y=\frac{k}{x} represents the relation where y is inversely proportional to x and k is the constant of proportionality.  

So our required equation would be d=\frac{k}{n}

Upon substituting our given values, we will get:

19=\frac{k}{35}

k=19\cdot 35

k=665

Since constant of proportionality is 665, so our equation would be d=\frac{665}{n}.

To find the number of days it will take to build a similar house with 5 workers, we will substitute n=5 in our equation as:

d=\frac{665}{5}

d=133

Therefore, it will take 133 days for 5 workers to build a similar house.

5 0
3 years ago
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