MHB Make x the subject of 2x/5-3b/4=x+5

[blackfriars]

hi to all
looking for some help to rearrange a formula to make x the subject
2x/5-3b/4=x+5

i moved +5 to the left and it became -5
i thought the negative 5 would cancel the denominator 5

this is what i thought i could do

2x-3b/4=x

-2x -2x

-3b/4 =-x
multiply both sides by -1 and the result i thought should be

3b/4=x
thanks in adv

 

[Wilmer]

Are you a student attending math classes?

 

[blackfriars]

Yes i am

 

[Greg]

$$\frac{2x}{5} - \frac{3b}{4}=x+5$$

To clear fractions, multiply both sides of the equation by $20$, the $\text{lcm}$ of $5$ and $4$:

$$8x-15b=20x+100$$

Rearrange so $x$ is on its own on one side of the equation:

$$-15b-100=20x-8x$$

Simplify:

$$-15b-100=12x$$

Divide through by $12$:

$$x=-\frac{15b+100}{12}$$

 

[blackfriars]

Thanks for that all i can do is learn
Cheers

 

[Wilmer]

i moved +5 to the left and it became -5
i thought the negative 5 would cancel the denominator 5

Make up a simple case:
x/5 = 5 : evident that x = 25, right?
Now, move the 5 as you did:
x/5 - 5 = 0 : ok?
Cancel the denominator with the -5:
x = 0
BUT x = 25 : convinced?