Question

4 1/2-5 1/3 : ( 20*x - 14 2/3) =1 5/6

Answer 1

Ответ: 5/6..........

Answer 2

To solve the equation, we need to find the value of 'x'. Let's first simplify the left-hand side of the equation:

4 1/2 - 5 1/3

To subtract these mixed fractions, we need to find a common denominator. The least common multiple (LCM) of 2 and 3 is 6.

4 1/2 = 4 + 1/2 = 8/2 + 1/2 = 9/2 5 1/3 = 5 + 1/3 = 15/3 + 1/3 = 16/3

Now, subtract:

9/2 - 16/3

To get a common denominator, multiply 9/2 by 3/3 and 16/3 by 2/2:

(9/2)(3/3) - (16/3)(2/2) = 27/6 - 32/6 = (27 - 32)/6 = -5/6

So, the left-hand side of the equation becomes:

-5/6 : (20*x - 14 2/3)

Now, let's simplify the right-hand side of the equation:

1 5/6

The value on the right-hand side is already in improper fraction form:

1 5/6 = 6/6 + 5/6 = 11/6

So, the equation now becomes:

-5/6 : (20*x - 14 2/3) = 11/6

To remove the fraction on the left side, we can multiply both sides by -6:

(-6) * (-5/6) : (20*x - 14 2/3) = (-6) * (11/6)

This simplifies to:

5 : (20*x - 14 2/3) = -11

Now, let's isolate the expression containing 'x':

20*x - 14 2/3 = 5/-11

To solve for 'x', we need to get rid of the constant term on the left side. First, let's convert 5/-11 to a mixed fraction:

5/-11 = -5/11

Now, add 14 2/3 to both sides:

20*x - 14 2/3 + 14 2/3 = -5/11 + 14 2/3

The left side simplifies to:

20*x = -5/11 + 14 2/3

Now, let's convert 14 2/3 to an improper fraction:

14 2/3 = 14 + 2/3 = 42/3 + 2/3 = 44/3

The equation becomes:

20*x = -5/11 + 44/3

To get a common denominator, multiply -5/11 by 3/3:

-5/11 * 3/3 = -15/33

The equation is now:

20*x = -15/33 + 44/3

To add these fractions, we need a common denominator, which is 33:

-15/33 + 44/3

To convert 44/3 to a fraction with a denominator of 33, multiply both the numerator and denominator by 11:

44/3 = (44 * 11) / (3 * 11) = 484/33

The equation becomes:

20*x = -15/33 + 484/33

Now, combine the fractions:

20*x = (484 - 15) / 33

20*x = 469 / 33

To solve for 'x', divide both sides by 20:

x = 469 / (20 * 33)

x = 469 / 660

x ≈ 0.7106 (rounded to four decimal places)

So, the value of 'x' that satisfies the equation is approximately 0.7106.