Question

How do you solve `2/3+5=20-b?`

Answer 1

`b = 14 1/3`

Explanation:

To solve the equation you need to re-arrange it so that you have:

`b = " a number"`

`2/3+5=20-b" "` simplifies to `" "5 2/3=20-b`

You have `-b` on the right hand side. Add `+b` to both sides:

`5 2/3color(blue)(+b)=20-b color(blue)(+b)" "larr (-b+b=0)`

Now subtract `color(magenta)(5 2/3)` from both sides

`5 2/3 color(magenta)(-5 2/3) +b=20 color(magenta)(-5 2/3)" "larr (5 2/3-5 2/3=0)`

`b = 14 1/3`

Answer 2

`b=43/3`

Explanation:

Let's multiply both sides of the equation by `3` to get rid of the fraction:

`3*2/3+5*3=20*3-3*b`

`2+15=60-3b`

`17=60-3b`

Now let's subtract `60` from both sides:

`17-60=60-3b-60`

`-43=-3b`

Now we can divide both sides by `-3` to solve for `b`:

`(cancel- 43)/(cancel- 3)=color(red)cancelcolor(red)-(cancel3 b)/(color(red)cancel- cancel3)`

`43/3=b/1`
`43/3=b`
OR,
`14 1/3=b`
OR,
`14.bar(33333)=b`