How Do You Solve the Equation x/5 - (2x+4)/3 = 1?

[tomtomtom1]

I have been struggling with this question can anyone explain how you would solve this, i have been told the answer is -5 but i want to know how to solve it.

Solve the following equation with algebraic fractions

x/5 - (2x+4)/3 = 1

 

[rock.freak667]

Expand out -(2x+4)/3 and then use your normal rules of algebra. Are you able to expand -(2x+4)/3 ?

 

[tomtomtom1]

is it 2x/3 + 4/3

 

[rock.freak667]

is it 2x/3 + 4/3

Right so (2x+5)/3 = 2x/3 + 4/3. If you put this into your equation you will have:

x/5 - (2x/3 +4/3) = 1


Can you simplify the left side of this equation using your standard algebra rules?

 

[tomtomtom1]

3x/15 - 10x/15 + 4/3

-7x/15 + 4/3 = 1

 

[rock.freak667]

3x/15 - 10x/15 + 4/3

-7x/15 + 4/3 = 1

For -(2x/3 + 4/3) you are essentially multiplying each term in the bracket by -1. So you should not have +4/3. What should you have instead? After you do that, make -7x/15 the subject of the formula.

 

[tomtomtom1]

got it

3x/15 - 10x/15 - 4/3 = 1
-7x/15 - 4/3 = 1
-7x/15 = 1 + 4/3
-7x = (1+4/3)*15
-7x = 15+(60/3)
-7x = 35
x = 35/-7
x = -5

Thanks