Question

How do you solve `43= - 5( y + 11) + 7y`?

Answer 1

`y=49`

Explanation:

First we switch sides from
`43=-5(y+11)+7y` to `-5(y+11)+7y=`.
We will remove the `7y` and the `43=` and focus on the rest.
We will distribute parentheses/brackets using:
`a(b+c)=ab+ac`.

`a` would be `-5`, `b` would be `y` and `c` would be `11` in this case.

Using `a(b+c)=ab+ac`, we know that `-5*y-5*11`. Multiply `-5*y=-5y` and `5*11=55`. Therefore the equation would be (with the `7y`) `-5y-55+7y`.

Next, we group like terms: `-5y+7y-55`, and then add `-5y+7y=2y`.
The whole equation will then be `2y-55=43`. Add `55` to both sides:

`2y-55color(blue)+color(blue)55=43color(blue)+color(blue)55` and simplify it to be `2y=98`.
Divide both sides by `2` and you get `y=49`.