Question

How do you solve `7= 12+ \frac { 1} { 2} a`?

Answer 1

`a = -10`

Explanation:

`7 = 12 + 1/2a`

`7 = 12 + a/2`

Multiply through with the LCM

`7 xx 2 = 12 xx 2 + a/2 xx 2`

`14 = 24 + a/cancel2 xx cancel2`

`14 = 24 + a`

Collect like terms

`a = 14 - 24`

`a = -10`

Answer 2

See a solution process below:

Explanation:

First, subtract `color(red)(12)` from each side of the equation to isolate the `a` term while keeping the equation balanced:

`-color(red)(12) + 7 = -color(red)(12) + 12 + 1/2a`

`-5 = 0 + 1/2a`

`-5 = 1/2a`

Now, multiply each side of the equation to by `color(red)(2)` to solve for `a` while keeping the equation balanced:

`color(red)(2) xx -5 = color(red)(2) xx 1/2a`

`-10 = cancel(color(red)(2)) xx 1/color(red)(cancel(color(black)(2)))a`

`-10 = 1a`

`-10 = a`

`a = -10`