Question

Решите уравнение: 8 7/18-(1 11/15 + х)= 3 4/15 + 2 13/45

Answer 1

8 7/18-1 11/15-х=49/15+103/45
-х=49/15+103/45-151/18+26/15
-х=294/90+206/90-755/90+156/90
-х=-99/90
х=99/90
х=1,1

Answer 2

-х=3 4/15+2 13/45+1 11/15-8 7/18
х=-3 4/15-2 13/45-1 11/15+8 7/18
х=-49/15-103/45-26/15+151/18
х=(-294-206-104+755)/90
х=151/90
х=1 61/90

Answer 3

8 + 7/18 - (1 + 11/15 + x) = 3 + 4/15 + 2 + 13/45

First, let's simplify the left side of the equation by adding the numbers and fractions separately:

8 + 7/18 - (1 + 11/15 + x) = 3 + 4/15 + 2 + 13/45 8 + 7/18 - 1 - 11/15 - x = 3 + 4/15 + 2 + 13/45 8 - 1 + 7/18 - 11/15 - x = 3 + 2 + 4/15 + 13/45 7 + 7/18 - 11/15 - x = 5 + 4/15 + 13/45

Now, let's find a common denominator for the fractions on both sides of the equation. The least common multiple of 18, 15, and 45 is 90.

Multiplying each fraction by the necessary factor to make the denominator 90:

7 * 90/18 + 7/18 - 11 * 6/15 - 6x/6 = 5 * 90/15 + 6 * 4/15 + 2 * 13/45 7 * 5 + 7/18 - 11 * 6 + 6x/6 = 5 * 6 + 6 * 4 + 2 * 13 35 + 7/18 - 66 + 6x/6 = 30 + 24 + 26 35 + 7/18 - 66 + 6x/6 = 80

Now, let's simplify the equation:

35 - 66 + 7/18 + 6x/6 = 80 -31 + 7/18 + x = 80

Now, let's isolate the variable x:

7/18 + x = 80 + 31 7/18 + x = 111

Subtract 7/18 from both sides:

x = 111 - 7/18 x = 1997/18

So the solution to the equation is: x = 1997/18