Question

1). (7x +1) - (9x +3) = 5 2). 3(6x-1) = 2(9x+1) - 103). 4(5x+2)=10(2x-3)+154). 2(7x - 7) = 7(2x-3) + 75). 3(x+6) = x +2(x+9)​

Answer 1

Ответ:

1). (7x +1) - (9x +3) = 5

7х+1-9х-3=5

7х-9х=5+3-1

-2х=7

2х=-7

х=-3.5

2). 3(6x-1) = 2(9x+1) - 10

18х-3=18х+2-10

18х-18х=-9+3

х=-6

3). 4(5x+2)=10(2x-3)+15

20х+8=20х-30+15

20х-20х=-30+15-8

х=-23

4). 2(7x - 7) = 7(2x-3) + 7

14х-14=14х-21+7

14х-14х=0

х=0

5). 3(x+6) = x +2(x+9)

3х+18=х+2х+18

6х=0

х=0

Answer 2

Let's solve each equation step by step:

1. $(7x + 1) - (9x + 3) = 5$

First, distribute the negative sign on the left side:

$7x + 1 - 9x - 3 = 5$

Now, combine like terms:

$(7x - 9x) + (1 - 3) = 5$

Simplify further:

$-2x - 2 = 5$

Add 2 to both sides to isolate the variable:

$-2x - 2 + 2 = 5 + 2$

$-2x = 7$

Now, divide both sides by -2 to find the value of x:

$x = -\frac{7}{2}$ or $x = -3.5$

2. $3(6x - 1) = 2(9x + 1) - 10$

First, distribute on both sides:

$18x - 3 = 18x + 2 - 10$

Now, combine like terms:

$18x - 3 = 18x - 8$

Subtract 18x from both sides to isolate the constant term:

$-3 = -8$

This equation has no solution because the variable $x$ cancels out.

3. $4(5x + 2) = 10(2x - 3) + 15$

First, distribute on both sides:

$20x + 8 = 20x - 30 + 15$

Now, combine like terms:

$20x + 8 = 20x - 15$

Subtract 20x from both sides to isolate the constant term:

$8 = -15$

This equation also has no solution because the variable $x$ cancels out.

4. $2(7x - 7) = 7(2x - 3) + 7$

First, distribute on both sides:

$14x - 14 = 14x - 21 + 7$

Now, combine like terms:

$14x - 14 = 14x - 14$

Subtract 14x from both sides to isolate the constant term:

$-14 = -14$

This equation is always true, which means it has infinitely many solutions. Any value of $x$ will satisfy this equation.

5. $3(x + 6) = x + 2(x + 9)$

First, distribute on both sides:

$3x + 18 = x + 2x + 18$

Now, combine like terms:

$3x + 18 = 3x + 18$

Subtract 3x from both sides to isolate the constant term:

$18 = 18$

This equation is also always true, which means it has infinitely many solutions. Any value of $x$ will satisfy this equation.

In summary, equations 2 and 3 have no solutions, and equations 4 and 5 have infinitely many solutions. Equation 1 has a single solution, $x = -\frac{7}{2}$.