How do i make X the subject

Question

3(x+2) + 4(x+5)/(x+7)=5

Answer 1

The question is ambiguous; it could be:

3(x+2)+(4(x+5)/(x+7))=5.

Let's try to solve this.

First we multiply through by x+7:

3(x+2)(x+7)+4(x+5)=5(x+7).

Now expand all the brackets:

3x^2+27x+42+4x+20=5x+35.

Gather like terms together:

3x^2+26x+27=0.

This does not factorise. The roots are irrational but can be found using the quadratic formula.

Let's try another interpretation:

(3(x+2)+4(x+5))/(x+7)=5.

Expand the brackets:

(3x+6+4x+20)/(x+7)=5

(7x+26)/(x+7)=5

Multiply through by (x+7):

7x+26=5x+35 so 2x=9 and x=9/2=4½ or 4.5.