Question

1. 6-х\3=х\72. х+5\6-х\5=13. х+х\9=24. 4х+4\8+5=9х\75. 4х-3\2-х\3=36. 4х-3(х-7)=2х+157. 2(х+1)+1\2(х-1)=7\48. 4х+2\3=2(х-2\3)9. -2\5х+6=1\2(х-1)10. 1 3\4 * корень 2\корень 9811. 1\корень18 + 1\корень 212. 2(3-5х)\2х+1\5 = -513 корень 0,48 * 1\корень 1214 2(х-3)\1\3х-1 = 415 0,5(х+1)-2х\-3(х+1)+4 = -2

Answer 1

1)6-x/3=x/7
6-x/3-x/7=0
42-7x/21-3x/21=0
2-10x=0
-10x=-2
x=0,2

3)x+x/9=2
2x/9=2
2x=18
x=9

Answer 2

To solve the given equations, let's go through each one step by step:

1. 6x/3 = x/72

To solve this equation, we'll start by cross-multiplying:

6x * 72 = 3 * x

432x = 3x

Dividing both sides of the equation by 3x, we get:

432 = 1/3

The equation has no solution since 432 does not equal 1/3.

2. x + 5/6 - x/5 = 13

To solve this equation, let's simplify the terms with x:

(x - x/5) + 5/6 = 13

(5x/5 - x/5) + 5/6 = 13

(4x/5) + 5/6 = 13

To get rid of the fractions, we'll find a common denominator, which is 30:

(24x/30) + (25/30) = 13

Combining like terms:

(24x + 25)/30 = 13

Multiplying both sides of the equation by 30:

24x + 25 = 390

Subtracting 25 from both sides:

24x = 365

Dividing both sides by 24:

x = 365/24

So the solution to the equation is x = 365/24.

3. x + x/9 = 24

To solve this equation, let's simplify the terms with x:

(9x + x)/9 = 24

10x/9 = 24

Multiplying both sides of the equation by 9:

10x = 216

Dividing both sides by 10:

x = 21.6

So the solution to the equation is x = 21.6.

4. 4x + 4/8 + 5 = 9x/75

To solve this equation, let's simplify the terms with x:

(4x - 9x/75) + 4/8 + 5 = 0

(300x - 9x + 150 + 600) / 600 = 0

(291x + 750) / 600 = 0

Multiplying both sides of the equation by 600:

291x + 750 = 0

Subtracting 750 from both sides:

291x = -750

Dividing both sides by 291:

x = -750/291

So the solution to the equation is x = -750/291.

5. 4x - 3/2 - x/3 = 36

To solve this equation, let's simplify the terms with x:

(12x - 3x - 2x)/6 = 36

7x/6 = 36

Multiplying both sides of the equation by 6:

7x = 216

Dividing both sides by 7:

x = 216/7

So the solution to the equation is x = 216/7.

6. 4x - 3(x - 7) = 2x + 15

To solve this equation, let's distribute -3 into (x - 7):

4x - 3x + 21 = 2x + 15

Combining like terms:

x + 21 = 2x + 15

Subtracting x from both sides:

21 = x + 15

Subtracting 15 from both sides:

6 = x

So the solution to the equation is x = 6.

7. 2(x + 1) + 1/2(x - 1) = 7/4

To solve this equation, let's simplify the terms with x:

(2x + 2) + (x - 1)/2 = 7/4

Multiplying both sides of the equation by 4 to get rid of the fraction:

8x + 8 + 2(x - 1) = 7

Distributing 2 into (x - 1):

8x + 8 + 2x - 2 = 7

Combining like terms:

10x + 6 = 7

Subtracting 6 from both sides:

10x = 1

Dividing both sides by 10:

x = 1/10

So the solution to the equation is x = 1/10.

8. 4x + 2/3 = 2(x - 2/3)

To solve this equation, let's distribute 2 into (x - 2/3):

4x + 2/3 = 2x - 4/3

Subtracting 2x from both sides:

2x + 2/3 = -4/3

Subtracting 2/3 from both sides:

2x = -4/3 - 2/3

2x = -6/3

Simplifying the right side:

2x = -2

Dividing both sides by 2:

x = -1

So the solution to the equation is x = -1.

9. -2/5x + 6 = 1/2(x - 1)

To solve this equation, let's distribute 1/2 into (x - 1):

-2/5x + 6 = 1/2x - 1/2

Adding 2/5x to both sides:

6 = 1/2x - 1/2 + 2/5x

Finding a common denominator of 10:

6 = 5/10x - 5/10 + 4/10x

Combining like terms:

6 = (5x - 5 + 4x)/10

6 = (9x - 5)/10

Multiplying both sides by 10:

60 = 9x - 5

Adding 5 to both sides:

65 = 9x

Dividing both sides by 9:

x = 65/9

So the solution to the equation is x = 65/9.

10. 1 + 3/4 + √(2/√98)

To solve this equation, let's simplify the terms:

1 + 3/4 + √(2/√98)

To simplify the square root, let's write it as a fraction:

1 + 3/4 + √(2/√(49 * 2))

Simplifying further:

1 + 3/4 + √(2/7√2)

To rationalize the denominator, let's multiply the numerator and denominator of the fraction by √7:

1 + 3/4 + √((2 * √7)/(7 * √2))

Simplifying further:

1 + 3/4 + √(2√7)/(7√2)

To combine the terms, we need to find a common denominator for 4 and 7√2:

(4 * 7√2)/(4 * 7√2) + (3 * 7√2)/(4 * 7√2) + √(2√7)/(7√2)

(28√2 + 21√2 + √(2√7))/(28√2)

Combining like terms:

(49√2 + √(2√7))/(28√2)

So the simplified form of the equation is 49√2 + √(2√7)/(28√2).

11. 1/√18 + 1/√21 + 1/√2 + 1/√212

To simplify this expression, let's rationalize the denominators:

1/√(9 * 2) + 1/√(7 * 3) + 1/√2 + 1/√212

1/(3√2) + 1/(√7 * √3) + 1/√2 + 1/(√2 * √106)

Multiplying the numerator and denominator of the first fraction by √2:

√2/(3 * 2) + 1/(√7 * √3) + 1/√2 + 1/(√2 * √106)

Simplifying further:

√2/6 + 1/(√7 * √3) + 1/√2 + 1/(√2 * √106)

To combine the terms, we need to find a common denominator for 6, √7 * √3, √2, and √2 * √106:

(√2 * √7 * √3 * √106)/(6 * √2 * √7 * √3 * √106) + (6 * √7 * √3)/(6 * √2 * √7 * √3) + (√2 * √7 * √3 * √106)/(√2 * √7 * √3 * √106) + (√2 * √7 * √3)/(√2 * √7 * √3 * √106)

(√2 * √7 * √3 * √106 + 6 * √7 * √3 + √2 * √7 * √3 * √106 + √2 * √7 * √3)/(6 * √2 * √7 * √3 * √106)

(