Question

Решите уравнения: 1) х+5/14=5/6; 2) 4 целых 5/19+х+1 целое 1/38=12 целых 1/2; 3) 17 целых 3/8-у=9 целых 5/12+2 целых 1/6; 4) 14 целых 9/16-х=6 целых 3/4+1 целое 2/5 Помогите пожалуйста срочно

Answer 1

1) х=5/6-5/14=35/42-15/42=20/42= 10/21

2) 4 целых 5/19+х+1 целое 1/38=12 целых 1/2;

81/19+х+39/38=25/2

   Х=25/2-81/19-39/38=475/38-162/38-39/38
   Х= 274/38=137/19= 7 4/19

3) 17 целых 3/8-у=9 целых 5/12+2 целых 1/6;

139/8-у=113/12+13/6

   У=139/8-113/12-13/6=417/24-226/24-52/24=139/24= 5 19/24

4) 14 целых 9/16-х=6 целых 3/4+1 целое 2/5 

233/16 –х=27/4+7/5 

Х=233/16-27/4-7/5=1165/80-540/80-112/80=513/80= 6 33/80

Answer 2

Solution to Equations:

1) To solve the equation x + 5/14 = 5/6, we can start by isolating the variable x on one side of the equation.

Subtracting 5/14 from both sides, we get:

x = 5/6 - 5/14

To find a common denominator, we can multiply the denominators 6 and 14:

x = (5/6) * (14/14) - (5/14) * (6/6)

Simplifying, we have:

x = 70/84 - 30/84

Combining the fractions, we get:

x = (70 - 30)/84

x = 40/84

Simplifying the fraction, we have:

x = 10/21

Therefore, the solution to the equation is x = 10/21.

2) The equation 4 целых 5/19 х + 1 целое 1/38 = 12 целых 1/2 involves mixed numbers. To solve it, we can convert the mixed numbers into improper fractions.

First, let's convert the mixed numbers into improper fractions:

4 целых 5/19 = (4 * 19 + 5)/19 = 81/19

1 целое 1/38 = (1 * 38 + 1)/38 = 39/38

Now, the equation becomes:

(81/19)х + (39/38) = (12 целых 1/2)

To simplify the equation, we can multiply through by the common denominator of 19 and 38, which is 722:

722 * (81/19)х + 722 * (39/38) = 722 * (12 целых 1/2)

Simplifying, we have:

722 * (81/19)х + 722 * (39/38) = 722 * (12 + 1/2)

Now, we can solve for x:

(722 * 81/19)х + (722 * 39/38) = (722 * 24 + 722 * 1/2)

Multiplying and simplifying, we get:

(722 * 81/19)х + (722 * 39/38) = 17328 + 361

Now, we can combine the fractions:

(722 * 81/19)х + (722 * 39/38) = 17689

To solve for x, we can isolate the variable:

(722 * 81/19)х = 17689 - (722 * 39/38)

Simplifying, we have:

(722 * 81/19)х = 17689 - 722 * 39/38

Now, we can solve for x by dividing both sides by (722 * 81/19):

х = (17689 - 722 * 39/38) / (722 * 81/19)

Calculating the right side of the equation, we get:

х ≈ -0.0004

Therefore, the solution to the equation is x ≈ -0.0004.

3) The equation 17 целых 3/8 - у = 9 целых 5/12 + 2 целых 1/6 involves mixed numbers. To solve it, we can convert the mixed numbers into improper fractions.

First, let's convert the mixed numbers into improper fractions:

17 целых 3/8 = (17 * 8 + 3)/8 = 139/8

9 целых 5/12 = (9 * 12 + 5)/12 = 113/12

2 целых 1/6 = (2 * 6 + 1)/6 = 13/6

Now, the equation becomes:

(139/8) - у = (113/12) + (13/6)

To simplify the equation, we can find a common denominator, which is 24:

24 * (139/8) - 24 * у = 24 * (113/12) + 24 * (13/6)

Simplifying, we have:

(24 * 139/8) - 24 * у = (24 * 113/12) + (24 * 13/6)

Now, we can solve for у:

(24 * 139/8) - 24 * у = (24 * 113/12) + (24 * 13/6)

Multiplying and simplifying, we get:

(24 * 139/8) - 24 * у = 3132 + 624

Now, we can combine the fractions:

(24 * 139/8) - 24 * у = 3756

To solve for у, we can isolate the variable:

-24 * у = 3756 - (24 * 139/8)

Simplifying, we have:

-24 * у = 3756 - 4176/8

Now, we can solve for у by dividing both sides by -24:

у = (3756 - 4176/8) / -24

Calculating the right side of the equation, we get:

у ≈ -3.625

Therefore, the solution to the equation is у ≈ -3.625.

4) The equation 14 целых 9/16 - х = 6 целых 3/4 + 1 целое 2/5 involves mixed numbers. To solve it, we can convert the mixed numbers into improper fractions.

First, let's convert the mixed numbers into improper fractions:

14 целых 9/16 = (14 * 16 + 9)/16 = 233/16

6 целых 3/4 = (6 * 4 + 3)/4 = 27/4

1 целое 2/5 = (1 * 5 + 2)/5 = 7/5

Now, the equation becomes:

(233/16) - х = (27/4) + (7/5)

To simplify the equation, we can find a common denominator, which is 80:

80 * (233/16) - 80 * х = 80 * (27/4) + 80 * (7/5)

Simplifying, we have:

(80 * 233/16) - 80 * х = (80 * 27/4) + (80 * 7/5)

Now, we can solve for х:

(80 * 233/16) - 80 * х = (80 * 27/4) + (80 * 7/5)

Multiplying and simplifying, we get:

(80 * 233/16) - 80 * х = 4860 + 1792

Now, we can combine the fractions:

(80 * 233/16) - 80 * х = 6652

To solve for х, we can isolate the variable:

-80 * х = 6652 - (80 * 233/16)

Simplifying, we have:

-80 * х = 6652 - 11620/16

Now, we can solve for х by dividing both sides by -80:

х = (6652 - 11620/16) / -80

Calculating the right side of the equation, we get:

х ≈ -0.081

Therefore, the solution to the equation is х ≈ -0.081.

I hope this helps! Let me know if you have any further questions.