Question

2/3 / 5/6х-1/6 +1/3=7/9

Answer 1

2/3/5/6х-1/6=7/9-1/3
2/3/5/6х-1/6=4/9
5/6х-1/6=2/3:4/9
5/6х-1/6=2/3*9/4
5/6х-1/6=3/2
5/6х=3/2+1/6
5/6х=10/6
Х=2

Answer 2

To solve this equation, we need to simplify both sides and then isolate the variable on one side.

First, we need to find a common denominator for the fractions on the left side. The least common multiple of 3, 6, and 9 is 18.

So, we can rewrite the equation as:

(4/6)/(5/6x) + (2/6)/(6x-1/6) + (6/18)/(1/3) = 7/9

Simplifying the left side:

(2/3) / (5/6x) + (1/3) / (6x - 1) + (1/3) / (1/3) = 7/9

Next, we can invert and multiply the second fraction on the left side:

(2/3) / (5/6x) + (1/3) * (6/6x - 1/6) + (1/3) / (1/3) = 7/9

Simplifying further:

(2/3) / (5/6x) + (6/18x - 1/18) + 1 = 7/9

Now, we can combine the fractions:

(2/3) / (5/6x) + (6/18x) - (1/18) + 1 = 7/9

And simplify:

(4/15x) + (1/3) = (2/9)

To isolate the variable, we can subtract 1/3 from both sides:

(4/15x) = (2/9) - (1/3)

Now, we can simplify the right side:

(4/15x) = (2/9) - (3/9)

(4/15x) = (-1/9)

Multiplying both sides by -9:

(-36/15x) = -1

Simplifying:

(12/5x) = 1

Multiplying both sides by 5x:

12 = 5x

Dividing both sides by 5:

x = 12/5

Therefore, the solution to the equation is x = 12/5.