Question

(х-5)/2=(9-х)/3,    (8+х)/7=(3х-5)/6,5

Answer 1

$1)3(x-5)=2(9-x)\\ 3x-15=18-2x\\ 5x=33\\ x=6.6\\\\2) (8+х)/7=(3х-5)/6,5\\ 6.5(8+x)=7(3x-5)\\ 52+6.5x=21x-35\\ 87=14.5x\\ x=6$

Answer 2

To solve the equations, let's find the values of x that satisfy them one by one.

1. (х-5)/2 = (9-х)/3

To eliminate the denominators, we can cross-multiply:

3(х-5) = 2(9-х)

Now, distribute the values:

3x - 15 = 18 - 2x

Now, isolate the variable x on one side:

3x + 2x = 18 + 15

5x = 33

Now, solve for x:

x = 33/5

x = 6.6

So, the solution for the first equation is x = 6.6.

2. (8+х)/7 = (3х-5)/6

Cross-multiply to eliminate the denominators:

6(8 + x) = 7(3x - 5)

Expand the terms:

48 + 6x = 21x - 35

Now, isolate the variable x on one side:

6x - 21x = -35 - 48

-15x = -83

Now, solve for x:

x = -83/-15

x = 5.53 (rounded to two decimal places)

So, the solution for the second equation is x = 5.53.

Remember to check your solutions by substituting them back into the original equations to make sure they are valid.