Question

1)27 : x + 405:9 = 48 2)613x - 54x = 8385 3)(27x -81): 3 = 18 4) (16x - 64): 7 = 64 5)86 - (2x + 15) = 39 6)2(3x + 70) = 350 7)6x + X-35 = 21 8) 17y + 14y = 279 9) 5y + 9y + 32 10) 200 + 28x + 35x = 504 11)203x - 184x = 608 12)305x - 16.3 = 1782​

Answer 1

Ответ:

1) 27 : x + 405:9 = 48

$\frac{27}{x} +45=48; \frac{27}{x} =48-45\\\\\frac{27}{x} =3; x=27:3; x =9$

2) 613x - 54x = 8385

559x = 8385; x = 15.

3) (27x -81): 3 = 18

$\frac{27x-81}{3} =18\\\\\frac{3(9x-27)}{3} =18\\\\9x-27=18; 9x=18+27; 9x=45;\\x=45:9; x=5$

4) (16x - 64): 7 = 64

$\frac{16x-64}{7}=64; | *7\\ 16x-64=448; 16x=448+64; 16x=512;\\x=512:16; x=32$

5) 86 - (2x + 15) = 39

86 - 2x - 15 = 39; -2x = 39 - 86 + 15;

-2x = -32; x = (-32) : (-2); x = 16.

6) 2(3x + 70) = 350

6x + 140 = 350; 6x = 350 - 140; 6x = 210; x = 210 : 6; x = 35.

7) 6x + X-35 = 21

7x - 35 = 21; 7x = 21 + 35; 7x = 56; x = 56 : 7; x = 8.

8) 17y + 14y = 279

31y = 279; y = 279 : 31; y = 9.

9) 5y + 9y + 32

14y + 32; 2(7y + 16).

10) 200 + 28x + 35x = 504

200 + 63x = 504; 63x = 504 - 200; 63x = 304;

$x=\frac{304}{63} =4\frac{52}{63} = 4,8254$

11) 203x - 184x = 608

19x = 608; x = 608 : 19; x = 32

12) 305x - 16.3 = 1782​

305x = 1782 + 16,3;

305x = 1798,3;

$x = \frac{17983}{10}:305; x = \frac{17983}{10}*\frac{1}{305} ;\\\\\\x = \frac{17983}{3050} = 5\frac{2733}{3050} = 5,9$

Answer 2

1) To solve the equation 27 + x + 405/9 = 48, we can start by simplifying the equation.

First, we can divide 405 by 9 to get 45. So the equation becomes: 27 + x + 45 = 48.

Next, we can combine like terms by adding 27 and 45: 72 + x = 48.

To isolate x, we can subtract 72 from both sides of the equation: x = 48 - 72.

Simplifying further, we get x = -24.

Therefore, the solution to the equation 27 + x + 405/9 = 48 is x = -24.

2) To solve the equation 613x - 54x = 8385, we can combine like terms on the left side of the equation.

Subtracting 54x from 613x gives us 559x. So the equation becomes: 559x = 8385.

To isolate x, we can divide both sides of the equation by 559: x = 8385/559.

Simplifying further, we get x = 15.

Therefore, the solution to the equation 613x - 54x = 8385 is x = 15.

3) To solve the equation (27x - 81)/3 = 18, we can start by simplifying the equation.

First, we can multiply both sides of the equation by 3 to get rid of the fraction. So the equation becomes: 27x - 81 = 54.

Next, we can add 81 to both sides of the equation: 27x = 135.

To isolate x, we can divide both sides of the equation by 27: x = 135/27.

Simplifying further, we get x = 5.

Therefore, the solution to the equation (27x - 81)/3 = 18 is x = 5.

4) To solve the equation (16x - 64)/7 = 64, we can start by simplifying the equation.

First, we can multiply both sides of the equation by 7 to get rid of the fraction. So the equation becomes: 16x - 64 = 448.

Next, we can add 64 to both sides of the equation: 16x = 512.

To isolate x, we can divide both sides of the equation by 16: x = 512/16.

Simplifying further, we get x = 32.

Therefore, the solution to the equation (16x - 64)/7 = 64 is x = 32.

5) To solve the equation 86 - (2x + 15) = 39, we can start by simplifying the equation.

First, we can simplify the expression inside the parentheses: 86 - 2x - 15 = 39.

Next, we can combine like terms by subtracting 15 from 86: 71 - 2x = 39.

To isolate x, we can subtract 71 from both sides of the equation: -2x = 39 - 71.

Simplifying further, we get -2x = -32.

To solve for x, we can divide both sides of the equation by -2: x = -32/-2.

Simplifying further, we get x = 16.

Therefore, the solution to the equation 86 - (2x + 15) = 39 is x = 16.

6) To solve the equation 2(3x + 70) = 350, we can start by simplifying the equation.

First, we can distribute the 2 into the parentheses: 6x + 140 = 350.

Next, we can subtract 140 from both sides of the equation: 6x = 350 - 140.

Simplifying further, we get 6x = 210.

To solve for x, we can divide both sides of the equation by 6: x = 210/6.

Simplifying further, we get x = 35.

Therefore, the solution to the equation 2(3x + 70) = 350 is x = 35.

7) To solve the equation 6x + X - 35 = 21, we can start by simplifying the equation.

First, we can combine like terms by adding 6x and X: 7x - 35 = 21.

Next, we can add 35 to both sides of the equation: 7x = 21 + 35.

Simplifying further, we get 7x = 56.

To solve for x, we can divide both sides of the equation by 7: x = 56/7.

Simplifying further, we get x = 8.

Therefore, the solution to the equation 6x + X - 35 = 21 is x = 8.

8) To solve the equation 17y + 14y = 279, we can combine like terms on the left side of the equation.

Adding 17y and 14y gives us 31y. So the equation becomes: 31y = 279.

To isolate y, we can divide both sides of the equation by 31: y = 279/31.

Simplifying further, we get y = 9.

Therefore, the solution to the equation 17y + 14y = 279 is y = 9.

9) To solve the equation 5y + 9y + 32 = 0, we can combine like terms on the left side of the equation.

Adding 5y and 9y gives us 14y. So the equation becomes: 14y + 32 = 0.

Next, we can subtract 32 from both sides of the equation: 14y = -32.

To solve for y, we can divide both sides of the equation by 14: y = -32/14.

Simplifying further, we get y = -16/7.

Therefore, the solution to the equation 5y + 9y + 32 = 0 is y = -16/7.

10) To solve the equation 200 + 28x + 35x = 504, we can combine like terms on the left side of the equation.

Adding 28x and 35x gives us 63x. So the equation becomes: 200 + 63x = 504.

Next, we can subtract 200 from both sides of the equation: 63x = 504 - 200.

Simplifying further, we get 63x = 304.

To solve for x, we can divide both sides of the equation by 63: x = 304/63.

Simplifying further, we get x = 4.825.

Therefore, the solution to the equation 200 + 28x + 35x = 504 is x = 4.825.

11) To solve the equation 203x - 184x = 608, we can combine like terms on the left side of the equation.

Subtracting 184x from 203x gives us 19x. So the equation becomes: 19x = 608.

To isolate x, we can divide both sides of the equation by 19: x = 608/19.

Simplifying further, we get x = 32.

Therefore, the solution to the equation 203x - 184x = 608 is x = 32.

12) To solve the equation 305x - 16.3 = 1782, we can start by simplifying the equation.

First, we can add 16.3 to both sides of the equation: 305x = 1782 + 16.3.

Simplifying further, we get 305x = 1798.3.

To solve for x, we can divide both sides of the equation by 305: x = 1798.3/305.

Simplifying further, we get x = 5.89.

Therefore, the solution to the equation 305x - 16.3 = 1782 is x = 5.89.