Question

-2 2/3 - x = 1 1/9 3(0,4 + 1,4)=х - 0,8 (2 7/9 z + 3 1/3)*3/5=1/6 z - 13/2

Answer 1

1)
$x = - \frac{23}{9}$
2)
$x = 6.2$
3)
$z = - 8 \frac{14}{23}$

Answer 2

To solve each of these equations, I'll go through them one by one:

1. -2 2/3 - x = 1 1/9

To solve for x, we need to isolate it on one side of the equation. First, let's convert both mixed numbers to improper fractions:

-2 2/3 = -8/3 1 1/9 = 10/9

Now, the equation becomes:

-8/3 - x = 10/9

Next, let's get rid of the fraction on the left side by multiplying everything by 9 (the common denominator of 3 and 9):

9 * (-8/3) - 9 * x = 9 * (10/9)

Simplifying:

-24/3 - 9x = 10

Now, combine the terms on the left side:

-8 - 9x = 10

Next, isolate x by moving -8 to the other side:

-9x = 10 + 8

-9x = 18

Finally, divide by -9 to solve for x:

x = 18 / -9

x = -2

So, the solution for x is -2.

2. 3(0.4 + 1.4) = х - 0.8

Let's first simplify the expression inside the parentheses:

0.4 + 1.4 = 1.8

Now, the equation becomes:

3(1.8) = х - 0.8

Next, simplify the left side:

3 * 1.8 = 5.4

Now, the equation is:

5.4 = х - 0.8

To solve for x, add 0.8 to both sides:

х = 5.4 + 0.8

х = 6.2

So, the solution for x is 6.2.

3. (2 7/9 z + 3 1/3) * 3/5 = 1/6 z - 13/2

First, convert the mixed numbers to improper fractions:

2 7/9 = 25/9 3 1/3 = 10/3

Now, the equation becomes:

(25/9 z + 10/3) * 3/5 = 1/6 z - 13/2

Next, distribute the 3/5 on the left side:

(3/5) * (25/9 z + 10/3) = 1/6 z - 13/2

(3/5) * (25/9 z) + (3/5) * (10/3) = 1/6 z - 13/2

Now, simplify the expressions on the left side:

(75/45 z) + (30/15) = 1/6 z - 13/2

(5/3 z) + 2 = 1/6 z - 13/2

Next, move the 1/6 z to the left side by subtracting 1/6 z from both sides:

(5/3 z) - (1/6 z) + 2 = - 13/2

To combine the z terms, find a common denominator for 3 and 6, which is 6:

(10/6 z) - (1/6 z) + 2 = - 13/2

Now, simplify the z terms:

(9/6 z) + 2 = - 13/2

Now, let's get rid of the fraction by multiplying everything by 6:

6 * [(9/6 z) + 2] = 6 * (- 13/2)

Simplify:

9z + 12 = -39

Next, isolate z by moving 12 to the other side:

9z = -39 - 12

9z = -51

Finally, divide by 9 to solve for z:

z = -51 / 9

z = -17/3

So, the solution for z is -17/3.