Question

8x+5(2-x)=13   (x-3)(5-x)>0

Answer 1

1) 8x+5*(2-x)=13            3) (x-3)*(5-x)>0

8x+10-5x=13                      -1(x-3)*(x-5)>0  |*(-1)

3x=13-10                                (x-3)*(x-5)<0  

x=1                                            x∈(3;5) 

Answer 2

Let's start by solving the first equation:

8x + 5(2 - x) = 13

8x + 10 - 5x = 13

3x + 10 = 13

3x = 3

x = 1

Therefore, x = 1 is the solution to the first equation.

Now let's solve the second inequality:

(x - 3)(5 - x) > 0

To find the values of x that make this inequality true, we need to consider the signs of the two factors on either side of zero.

When x < 3, both factors are negative, so the product is positive.

When 3 < x < 5, the first factor is negative and the second factor is positive, so the product is negative.

When x > 5, both factors are positive, so the product is positive.

Therefore, the solution to the inequality is:

x < 3 OR x > 5

Putting this together with the solution to the first equation, we have:

x = 1 AND (x < 3 OR x > 5)

So the final solution is:

x = 1.