Question

839. Решите уравнения: 1) 3х - 15 = x+ 3; 2) 7 - 3x = x + 11; 3) 2(х + 3) = x + 13; 4) 4(5 - x) = 3х – 1; 5) 3(х – 2) =х+4; 6) 5(x-1) = 4х +3.

Answer 1

Пошаговое объяснение:

1)

$3x-15=x+3;\\3x-x=3+15;\\2x=18;\\x=18:2;\\x=9.$

Ответ: 9.

2)

$7-3x=x+11;\\-3x-x= 11-7;\\-4x=4;\\x=4:(-4);\\x=-1.$

Ответ: -1.

3)

$2(x+3) =x+13;\\2x+6=x+13;\\2x-x=13-6;\\x=7.$

Ответ: 7.

4)

$4(5-x)= 3x-1;\\20-4x=3x-1;\\-4x-3x=-1-20;\\-7x=-21|*(-1);\\7x=21;\\x=21:7;\\x=3.$

Ответ: 3.

5)

$3(x-2)=x+4;\\3x-6=x+4;\\3x-x=4+6;\\2x=10;\\x=10:2;\\x=5.$

Ответ: 5.

6)

$5(x-1) =4x+3;\\5x-5=4x+3;\\5x-4x=3+5;\\x=8.$

Ответ: 8.

Answer 2

1. 3x - 15 = x + 3

First, let's simplify the equation by combining like terms:

3x - x = 3 + 15 2x = 18

Now, divide both sides of the equation by 2 to solve for x:

2x/2 = 18/2 x = 9

Therefore, the solution to the equation is x = 9.

2. 7 - 3x = x + 11

Let's simplify the equation:

7 - 11 = 3x + x -4 = 4x

Divide both sides of the equation by 4:

-4/4 = 4x/4 -1 = x

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

3. 2(x + 3) = x + 13

Expanding the left side of the equation:

2x + 6 = x + 13

Next, subtract x from both sides of the equation:

2x - x + 6 = x - x + 13 x + 6 = 13

Now, subtract 6 from both sides of the equation:

x + 6 - 6 = 13 - 6 x = 7

The solution to the equation is x = 7.

4. 4(5 - x) = 3x - 1

Expanding the left side of the equation:

20 - 4x = 3x - 1

Next, add 4x to both sides of the equation:

20 - 4x + 4x = 3x - 1 + 4x 20 = 7x - 1

Now, add 1 to both sides of the equation:

20 + 1 = 7x - 1 + 1 21 = 7x

Finally, divide both sides of the equation by 7:

21/7 = 7x/7 3 = x

Therefore, the solution to the equation is x = 3.

5. 3(x - 2) = x + 4

Expanding the left side of the equation:

3x - 6 = x + 4

Next, subtract x from both sides of the equation:

3x - x - 6 = x - x + 4 2x - 6 = 4

Now, add 6 to both sides of the equation:

2x - 6 + 6 = 4 + 6 2x = 10

Finally, divide both sides of the equation by 2:

2x/2 = 10/2 x = 5

So the solution to the equation is x = 5.

6. 5(x - 1) = 4x + 3

Expanding the left side of the equation:

5x - 5 = 4x + 3

Next, subtract 4x from both sides of the equation:

5x - 4x - 5 = 4x - 4x + 3 x - 5 = 3

Now, add 5 to both sides of the equation:

x - 5 + 5 = 3 + 5 x = 8

Therefore, the solution to the equation is x = 8.

To summarize the solutions:

1. x = 9
2. x = -1
3. x = 7
4. x = 3
5. x = 5
6. x = 8