Question

How do you solve `19a - 3(a - 6) = 66` for `a`?

Answer 1

See a solution process below:

Explanation:

First expand the term in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

`19a - color(red)(3)(a - 6) = 66`

`19a - (color(red)(3) * a) + (color(red)(3) * 6) = 66`

`19a - 3a + 18 = 66`

Next, combine like terms:

`(19 - 3)a + 18 = 66`

`16a + 18 = 66`

Then, subtract `color(red)(18)` from each side of the equation to isolate the `a` term while keeping the equation balanced:

`16a + 18 - color(red)(18) = 66 - color(red)(18)`

`16a + 0 = 48`

`16a = 48`

Now, divide each side of the equation by `color(red)(16)` to solve for `a` while keeping the equation balanced:

`(16a)/color(red)(16) = 48/color(red)(16)`

`(color(red)(cancel(color(black)(16)))a)/cancel(color(red)(16)) = 3`

`a = 3`

Answer 2

`a = 3`

Explanation:

`19a - 3(a-6) = 66`

`19a - 3a + 18 = 66`

`19a - 3a color(red)(cancel(color(black)(+ 18) - 18)) = 66 color(red)(- 18)`

`19a - 3a = 66 - 18`

`16a = 66 - 18`

`16a = 48`

`color(red)(cancel(color(black)(16))) a color(red)(cancel(÷ 16)) = 48 ÷ 16`

`a = 48 ÷ 16`

`color(blue)(a = 3`

We can substitute `a` for `3` to prove our answer.

`19 xx 3 - 3(3 - 6) = 66`

`19 xx 3 - 3 xx -3 = 66`

`57 - 3 xx -3 = 66`

`57 - -9 = 66`

`57 + 9 = 66`