Question

Решите уравнения :1). 5x+4=x+12; 2) 13-5y=8-2y; 3) 5x+(3x-7)=9; 4) 3y-(5-y)=11; 5) (7a+1)-(6a+3)=5; 6) (8s+11)-113=9s-5

Answer 1

Решение:

1) 5х+4 = х+12

5х-х = 12-4

4х = 8

х = 8/4

х = 2;

2) 13-5у = 8-2у

-5у+2у = 8-13

-3у = -5

у = 5/3;

3) 5х+(3х-7) = 9

5х+3х-7 = 9

5х+3х = 9+7

8х = 16

х = 16/8

х = 2;

4) 3у-(5-у) = 11

3у-5+у = 11

3у+у = 11+5

4у = 16

у = 16/4

у = 4;

5) (7а+1)-(6а+3) = 5

7а+1-6а-3 = 5

7а-6а = 5-1+3

а = 7;

6) (8s+11)-113 = 9s-5

8s+11-113 = 9s-5

8s-9s = -5-11+113

-s = 97

s = -97

Answer 2

1) 4x=8

x=2

2) 7y=-21

y=-3

3)8x=16

x=2

4)4y=16

y=4

5) a=7

6) s=-107

Answer 3

1. 5x + 4 = x + 12

To solve this equation, we need to isolate the variable x. Let's simplify the equation step by step:

Subtract x from both sides: 5x - x + 4 = x - x + 12 4x + 4 = 12

Subtract 4 from both sides: 4x + 4 - 4 = 12 - 4 4x = 8

Divide both sides by 4: (4x)/4 = 8/4 x = 2

So the solution to the equation is x = 2.

2. 13 - 5y = 8 - 2y

To solve this equation, we'll follow a similar process:

Subtract 8 from both sides: 13 - 5y - 8 = 8 - 8 - 2y 5 - 5y = -2y

Add 2y to both sides: 5 - 5y + 2y = -2y + 2y 5 - 3y = 0

Subtract 5 from both sides: 5 - 3y - 5 = 0 - 5 -3y = -5

Divide both sides by -3 (or multiply both sides by -1/3 to simplify): (-3y)/-3 = (-5)/-3 y = 5/3 or y = 1.67

So the solution to the equation is y = 5/3 or y = 1.67.

3. 5x + (3x - 7) = 9

Let's simplify the equation step by step:

Remove the parentheses using the distributive property: 5x + 3x - 7 = 9

Combine like terms: 8x - 7 = 9

Add 7 to both sides: 8x - 7 + 7 = 9 + 7 8x = 16

Divide both sides by 8: (8x)/8 = 16/8 x = 2

So the solution to the equation is x = 2.

4. 3y - (5 - y) = 11

Let's simplify the equation step by step:

Remove the parentheses using the distributive property: 3y - 5 + y = 11

Combine like terms: 4y - 5 = 11

Add 5 to both sides: 4y - 5 + 5 = 11 + 5 4y = 16

Divide both sides by 4: (4y)/4 = 16/4 y = 4

So the solution to the equation is y = 4.

5. (7a + 1) - (6a + 3) = 5

Let's simplify the equation step by step:

Remove the parentheses using the distributive property: 7a + 1 - 6a - 3 = 5

Combine like terms: (7a - 6a) + (1 - 3) = 5 a - 2 = 5

Add 2 to both sides: a - 2 + 2 = 5 + 2 a = 7

So the solution to the equation is a = 7.

6. (8s + 11) - 113 = 9s - 5

Let's simplify the equation step by step:

Remove the parentheses: 8s + 11 - 113 = 9s - 5

Combine like terms: 8s - 102 = 9s - 5

Subtract 8s from both sides: 8s - 8s - 102 = 9s - 8s - 5 -102 = s - 5

Add 5 to both sides: -102 + 5 = s - 5 + 5 -97 = s

So the solution to the equation is s = -97.