how do you do this math problem and others like it?

Question

8 over 5x - 2 over 3x = 4 over 15

Answer 1

8/5x-2/3x=4/15
multiply by 15x
24-10=4x
4x=14
dividing by 4
x=3 1/2
ifit is (8/5)x-(2/3)x=4/15
multiply by 15
24x-10x=4
14x=4
dividing by 14
x=4/14
=2/7

Answer 2

8...... - 2 ............. 4
---..... ----- ..... = ------
5x .... 3x .......... 15


First make sure the denominators on the Left Hand side of the equation are the same. To do this, take the LCM of the denominator. ( Least Common Multiple ). In this case it would be 15x. If we change the denominator we would also have to change the numerator to keep the value of the fraction consistent.

8....... -.. 2........... 4
----- ... ----- .... = ------
5x ...... 3x ........... 15

To make 5x, 15x we multiplied it by 3. So, we also need to multiply the numerator by 3 to keep its value the same.

To make 3x, 15x we multiplied it by 5. So, we also need to multiply the numerator by 5 to keep its value the same.

So, we would get the following:
8 *3......... - 2*5 .......... 4
----- .......... -----... = ------
15x ......... .. 15x .......... 15


or



24.. - .....10 ......... 4
----- ....... ----- ..... = ------
15x .........5x ........... 15

14 ... =... 4
------... ----
15x ... ..15

We can multiply both sides of the equation by 15. ( remember if we do something to one side of the equation we need to do that to the other side of the equation also ) ( We multiply with a 15, because by multiplying , with 15, we get a 15 on the numerators of both sides of the equation, and so we can cancel the 15 on the numerators with the 15 on the denominators )

14 ... = .. 4
----- ... ----
x ...... 1

cross multiply
14 * 1 = 4 * x

14 = 4x

14.. = x
---
4

7 = x
--
2

How you do problems like these???? Try to simplify the equation by sticking to the rules. Eventually the problem becomes smaller and smaller and you can solve it.

Answer 3

8/5x - 2/3x = 4/15

15x(8/5x) - 15x(2/3x) = 15x(2/15)

24 - 10 = 60x/15

14 = 4x

14/4 = 4x/4

3 2/4 = x

3 1/2 = x

3.5 = x

The answer is x = 3.5

Insert the x value into the equation

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Check

8/5x - 2/3x = 4/15

8/5(3.5) - 2/3(3.5) = 4/15

8 / 17.5 - 2 / 10.5 = 4/15

0.457142857 - 0.19047619 = 0.2666666667

0.2666666667 = 0.2666666667

- - - - - - - s-

Answer 4

8/5x-2/3x=4/15;
u'll find first the LCD to subtract the numerators the answer will be ;

24-10/15x since (15x is the LCD) hence after;

14/15x=4/15

then u should be able to equate /get the value of x thus,

x=2/7 how?

14/15x was being divided to 4/15setting x to the left.....

NOTE: pls. solve this through long form division, i mean not the horizontal form of dividing.........

Answer 5

8/(5x-2/3x) = 4/15
multiply both sides by 15 yielding 120/(5X-2/3X) = 4
multiply both sides by (5x-2/3x) yielding 120 = 4(5x-2/3x)
divide both sides by 4 yielding 30 = 5x-2/3x
multiply both sides by 3x yielding 90x = 15x^2 - 2
subtract 90x from both sides yielding 0 = 15^2 -90x -2
recognize this as a quadratic and substitute the coefficients into the quadratic solution x = (-b +/- (b^2 - 4ac)^1/2))/2a yielding x = -.022140522 and x = 6.022140522...

note: both solutions work in the original equation
note: x^2 means x squared and (x)^1/2 means the square root of x

Answer 6

8/5x - 2/3x = 4/15
Multiplying through by LCD (15x),
3*8 - 5*2 = 4x
x = (24 - 10)/4
x = 7/2 = 3.5

Answer 7

(8/5x)-(2/3x)=4/15
([24-10]/15x=4/15
14/x=4
4x=14
x=14/4=7/2=3 1/2

Answer 8

8/(5x-2)/3x=4/15
15*3x*(8/(5x-2)/3x)=15*3x(4/15)
120/(5x-2)=12x
10*(5x-2)=x
50x-20=x
49x=20
x=20/49