Question

1).6(х – 3) = 12 2).14 = 7(х + 2)3).12х + 4 = 3(4х – 2)4).3х + (2х – 1) = 105).(3х – 2) – (х – 1) = 106).2(х – 1) – 4 = 6(х + 2)7).6х – 3(х – 1) = 4 + 5х8).5х + 18 = 7х + 6(3х – 7)​

Answer 1

1) 6(х-3)=12

6х-18=12

6х=12+18

6х=30

х=30÷6

х=5

2) 14=7(х+2)

7х+14=14

7х=14-14

7х=0

х=0÷7

х=0

3) 12х+4=3(4х-2)

12х+4=12х-6

12х-12х=-6-4

0=-10

корней нет

4) 3х+(2х-1)=10

3х+2х-1=10

3х+2х=10+1

5х=11

х=11÷5

х=2,2

5) (3х-2)-(х-1)=10

3х-2-х+1=10

3х-х=10+2-1

2х=11

х=11÷2

х=5,5

6) 2(х-1)-4=6(х+2)

2х-2-4=6х+12

2х-6х=12+2+4

-4х=18

х=18÷(-4)

х=-4,5

7) 6х-3(х-1)=4+5х

6х-3х+3=4+5х

6х-3х-5х=4-3

-2х=1

х=1÷(-2)

х=-0,5

8) 5х+18=7х+6(3х-7)

5х+18=7х+18х-42

5х-7х-18х=-42-18

-20х=-60

х=-60÷(-20)

х=3

Answer 2

It looks like you have a set of linear equations. Let's go through each equation and solve for the variable $x$ in each case:

1. $6(x - 3) = 12$ Distribute the 6: $6x - 18 = 12$ Add 18 to both sides: $6x = 30$ Divide by 6: $x = 5$

2. $14 = 7(x + 2)$ Divide both sides by 7: $2 = x + 2$ Subtract 2 from both sides: $x = 0$

3. $12x + 4 = 3(4x - 2)$ Distribute the 3: $12x + 4 = 12x - 6$ Subtract $12x$ from both sides: $4 = -6$ Since this leads to a contradiction ($4 = -6$ is not true), there is no solution.

4. $3x + (2x - 1) = 10$ Combine like terms: $5x - 1 = 10$ Add 1 to both sides: $5x = 11$ Divide by 5: $x = 11/5$

5. $3x - 2 - (x - 1) = 10$ Distribute the negative sign: $3x - 2 - x + 1 = 10$ Combine like terms: $2x - 1 = 10$ Add 1 to both sides: $2x = 11$ Divide by 2: $x = 11/2$

6. $2(x - 1) - 4 = 6(x + 2)$ Distribute the 2 and 6: $2x - 2 - 4 = 6x + 12$ Combine like terms: $2x - 6 = 6x + 12$ Subtract $2x$ from both sides: $-6 = 4x + 12$ Subtract 12 from both sides: $-18 = 4x$ Divide by 4: $x = -18/4$

7. $6x - 3(x - 1) = 4 + 5x$ Distribute the -3: $6x - 3x + 3 = 4 + 5x$ Combine like terms: $3x + 3 = 4 + 5x$ Subtract $3x$ from both sides: $3 = 4 + 2x$ Subtract 4 from both sides: $-1 = 2x$ Divide by 2: $x = -1/2$

8. $5x + 18 = 7x + 6(3x - 7)$ Distribute the 6: $5x + 18 = 7x + 18x - 42$ Combine like terms: $5x + 18 = 25x - 42$ Subtract $5x$ from both sides: $18 = 20x - 42$ Add 42 to both sides: $60 = 20x$ Divide by 20: $x = 3$

So, the solutions for each equation are as follows:

1. $x = 5$
2. $x = 0$
3. No solution
4. $x = \frac{11}{5}$
5. $x = \frac{11}{2}$
6. $x = -\frac{9}{2}$
7. $x = -\frac{1}{2}$
8. $x = 3$