Question

15( a+2)=6(2a+7) 3x=6/7 7y+4,9=0 1,5-3z=6-5,5z 2(3x-2)=3(8-2x) |x-4|=10

Answer 1

15(а+2) = 6(2а + 7)
15а + 15*2  = 6 * 2а + 6*7
15а + 30  = 12а + 42
15а - 12а = 42 - 30
3а = 12
а = 12:3
а= 4
проверка:
15(4 + 2) = 6(2*4 + 7 )
15 * 6  =  6  *15
90=90

3х =6/7
х= 6/7  : 3 = 6/7  * 1/3 
х= 2/7
проверка:
3  *  2/7  = 3/1  * 2/7  = 6/7

7у  + 4,9  = 0
7у  =  - 4,9
у=  - 4,9 : 7
у= - 0,7
проверка:
7 * (-0,7)  + 4,9   =  - 4,9  + 4,9  = 0

1,5  - 3z= 6  - 5.5z
-3z  + 5.5z  =  6 - 1.5
2.5z  = 4,5
z = 4,5 : 2,5
z = 1,8
проверка:
1,5  - 3*1,8   = 6  - 5,5 * 1,8
1,5  -  5,4  =  6  -  9,9
- 3,9  = -3,9

2(3х - 2) = 3(8 - 2х)
6х  -  4  = 24  - 6х
6х  + 6х = 24  + 4
12х = 28
х = 28/12  = 7/3
х = 2 целых  1/3
проверка:
2 ( 3  * (7/3)  - 2)  = 3(8  -  2  *  (7/3))
2 * ( 7  -  2)  = 3(24/3    -  14/3)
2 * 5    =  3   *  (10/3)
10  = 10

|x  - 4|  = 10
x  - 4  = 10
x =  10  + 4
x₁ = 14
x  - 4  =  - 10
x =  - 10 + 4
x₂ =  - 6
проверка:
| 14  - 4 | = 10
| - 6  - 4|  = | - 10|  = 10

Answer 2

15(а+2)=6(2а+7)
15а+30=12а+42
3а=12
а=4;
3х=6/7
21х=6
х=6/21;
7y+4,9=0
7y=-4,9
y=0,7;
1,5-3z=6-5,5z
2.5z=4,5
z=1,8;
2(3x-2)=3(8-2x)
6x-4=24-6x
12x=28
x=2;
|a-4|=10
a>=0;a-4=10
a=6
a<=0;-a+4=10
a=-6

Answer 3

Let's solve each equation step-by-step:

1. 15(a + 2) = 6(2a + 7)

To solve this equation, distribute the numbers inside the parentheses and then combine like terms:

15a + 30 = 12a + 42

Now, let's move all the 'a' terms to one side and constants to the other side:

15a - 12a = 42 - 30

3a = 12

Finally, solve for 'a':

a = 12 / 3

a = 4

2. 3x = 6/7

To solve for 'x', divide both sides by 3:

x = (6/7) / 3

x = 6/7 * 1/3

x = 6/21

x = 2/7

3. 7y + 4.9 = 0

To solve for 'y', first, subtract 4.9 from both sides:

7y = -4.9

Now, divide by 7:

y = -4.9 / 7

y ≈ -0.7

4. 1.5 - 3z = 6 - 5.5z

To solve for 'z', first, combine like terms:

1.5 + 5.5z = 6 - 3z

Now, move all the 'z' terms to one side and constants to the other side:

5.5z + 3z = 6 - 1.5

8.5z = 4.5

Finally, solve for 'z':

z = 4.5 / 8.5

z ≈ 0.529

5. 2(3x - 2) = 3(8 - 2x)

Expand both sides of the equation:

6x - 4 = 24 - 6x

Now, move all the 'x' terms to one side and constants to the other side:

6x + 6x = 24 + 4

12x = 28

Finally, solve for 'x':

x = 28 / 12

x ≈ 2.333

6. |x - 4| = 10

To solve for 'x', we need to consider two cases:

Case 1: x - 4 = 10 Add 4 to both sides: x = 10 + 4 x = 14

Case 2: -(x - 4) = 10 Distribute the negative sign: -x + 4 = 10 Subtract 4 from both sides: -x = 6 Multiply by -1 to isolate 'x': x = -6

So, there are two possible solutions for 'x': x = 14 and x = -6.

I hope this helps! If you have any more equations or questions, feel free to ask.