Question

1) -2z-(-4z-3)=4 2) -6z-(-5-z)=-10 3) y-1+(y-2)=-4-(y-3) 4) 3z+5=-(-2z-7)+18 1)Стол из 6 стульев стоят 848. Стул на 8 дешевле, чем стол. Сколько стоит стул и сколько стол?

Answer 1

Пусть 1 часть будет Х, тогда
(стульев ВСЕГО 6) стульев ВСЕГО 6Х (1СТУЛ=х), стол Х+8 (так как стул НА 8 дешевле)
составляем уравнение
6Х+Х+8=848
7Х+8=848
7Х=848-8
7Х=840
х=120 (1часть)
ответ:
СТОЛ=128;
1 Стул 120. (6 СТУЛЬЕВ 720)
ПРОВЕРКА (720+1128=848)

Answer 2

1)  $-2z-(-4z-3)=4$
    $-2z+4z+3=4$
    $2z+3=4$
    $2z=4-3$
    $2z=1$
    $z=0.5$
2)  $-6z-(-5-z)=-10$
     $-6z+5+z=-10$
     $-5x+5=-10$
     $-5x=-10-5$
     $-5x=-15$
     $x=3$
3)  $y-1+(y-2)=-4-(y-3)$
     $y-1+y-2=-4-y+3$
     $2y-3=-1-y$
     $2y+y=-1+3$
     $3y=2$
     $y= \frac{2}{3}$
4)  $3z+5=-(-2z-7)+18$
     $3z+5=2z+7+18$
     $3z+5=2z+25$
     $3z-2z=25-5$
     $z=20$

Answer 3

1. Let's simplify the equation step by step:

-2z - (-4z - 3) = 4

First, distribute the negative sign inside the parentheses:

-2z + 4z + 3 = 4

Combine like terms:

2z + 3 = 4

Next, isolate the variable by subtracting 3 from both sides:

2z = 4 - 3

2z = 1

Finally, divide both sides by 2 to solve for z:

z = 1/2

Therefore, the solution to the equation is z = 1/2.

2. Let's simplify the equation step by step:

-6z - (-5 - z) = -10

First, distribute the negative sign inside the parentheses:

-6z + 5 + z = -10

Combine like terms:

-5z + 5 = -10

Next, isolate the variable by subtracting 5 from both sides:

-5z = -10 - 5

-5z = -15

Finally, divide both sides by -5 to solve for z:

z = (-15) / (-5)

z = 3

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

3. Let's simplify the equation step by step:

y - 1 + (y - 2) = -4 - (y - 3)

First, simplify the expressions within the parentheses:

y - 1 + y - 2 = -4 - y + 3

Combine like terms:

2y - 3 = -4 - y + 3

Rearrange the terms:

2y + y = -4 + 3 + 3

Combine like terms:

3y = 2

Finally, divide both sides by 3 to solve for y:

y = 2/3

Therefore, the solution to the equation is y = 2/3.

4. Let's simplify the equation step by step:

3z + 5 = -(-2z - 7) + 18

First, distribute the negative sign inside the parentheses:

3z + 5 = 2z + 7 + 18

Combine like terms:

3z + 5 = 2z + 25

Next, isolate the variable by subtracting 2z from both sides:

3z - 2z + 5 = 2z - 2z + 25

z + 5 = 25

Finally, subtract 5 from both sides to solve for z:

z = 25 - 5

z = 20

Therefore, the solution to the equation is z = 20.

Now let's solve the pricing problem:

Let the cost of a chair be x and the cost of a table be y.

From the given information, we have two equations:

6x + y = 848 (equation 1) x = y - 8 (equation 2)

We can substitute equation 2 into equation 1:

6(y - 8) + y = 848

Simplify the equation:

6y - 48 + y = 848

Combine like terms:

7y - 48 = 848

Add 48 to both sides:

7y = 848 + 48

7y = 896

Divide both sides by 7 to solve for y:

y = 896 / 7

y ≈ 128

Substitute the value of y back into equation 2 to find x:

x = 128 - 8

x = 120

Therefore, the chair costs approximately 120 and the table costs approximately 128.