Question

How do you solve `(b-7)/4=(b+9)/7`?

Answer 1

`85/3`

Explanation:

Common denominator: LCM of 4 and 7 is 28, or `4xx7`
Therefore, we can rewrite the equation as the following:
`(7(b-7))/28=(4(b+9))/28` which simplifies to `(7b-49)/28=(4b+36)/28`

Now let's separate the variables. Rewrite again:
`(7b)/28-49/28=(4b)/28+36/28`

Put the like terms with each other.
`(7b)/28-(4b)/28=49/28+36/28`

Take out the denominator since they're all equivalent anyway.
`7b-4b=49+36`
Simplify: `3b=85`

Divide to isolate variable: `b=85/3`