Question

853. При каком значении переменной равны значения выражений: 1) 6 1/3z + 4 1/7 и 3 1/6 + ,5 1/6z??​

Answer 1

Ответ:

6 1/3z+4 1/7 = 3 1/6+5 1/6z

6 1/3z-5 1/6z=3 1/6- 4 1/7

6 2/6z - 5 1/6z = 3 7/42 - 4 6/42

1 1/6 z= -41/42

z = - 41/42÷ 7/6

z= -41/42×6/7

z= - 41/49

Answer 2

The Value of the Variable

To find the value of the variable that makes the two expressions equal, let's consider the given expressions:

1) 6 + 1/3z + 4 + 1/7 2) 3 + 1/6 + 5 + 1/6z

We want to find the value of 'z' that makes these two expressions equal.

To solve this, we can set the two expressions equal to each other and solve for 'z':

6 + 1/3z + 4 + 1/7 = 3 + 1/6 + 5 + 1/6z

To simplify the equation, we can combine like terms:

10 + 1/3z + 1/7 = 8 + 1/6 + 1/6z

Now, let's find a common denominator for the fractions. The least common multiple of 3, 6, and 7 is 42. Multiplying each fraction by the appropriate factor to get a denominator of 42, we get:

(10 * 42) + (1/3z * 42) + (1/7 * 42) = (8 * 42) + (1/6 * 42) + (1/6z * 42)

420 + 14z + 6 = 336 + 7 + 7z

Combine like terms:

420 + 14z + 6 = 343 + 7z

Simplify:

14z + 426 = 350 + 7z

Subtract 7z from both sides:

14z - 7z + 426 = 350

Combine like terms:

7z + 426 = 350

Subtract 426 from both sides:

7z = 350 - 426

Simplify:

7z = -76

Divide both sides by 7:

z = -76/7

Therefore, the value of the variable 'z' that makes the two expressions equal is z = -76/7.