Question

Imagine you are teaching a fellow student how to solve:
2(x + 6) − 10 = 12 + 4(x − 1)

In your own words, explain the process for solving this equation. Please include your work at each step of the process along with the final answer.

Answer 1

You need to first distribute the numbers outside the parenthesis...into the parenthesis...this means you take that number...and multiply it by each term in the parenthesis...so

2(x + 6) − 10 = 12 + 4(x − 1)
( ^ )

is

2 times x = ?
2 times 6 = ?

The answer to those 2 questions are...

2x
and
12

so now we have

2x + 12 − 10 = 12 + 4(x − 1)
( ^ )

this one is written as

4 times x = ?
4 times -1 = ?

the answer to THOSE 2 questions are

4x
and
-4

so now we have

2x + 12 − 10 = 12 + 4x − 4

Now...we want to combine all the numbers with an 'x' next to them....we can do this by subtracting 4x from both sides of the equation

2x + 12 − 10 = 12 + 4x − 4
-4x -4x

-2x + 12 - 10 = 12 - 4

Now we want to just combine all the other numbers

-2x + 12 - 10 = 12 - 4
( ^ ) ( ^ )

12 - 10 is 2.......and 12 - 4 is 8 so now we have

-2x + 2 = 8

Now we want to combine for the last time the numbers without the 'x' next to them
so lets subtract 2 from both sides of this equation

-2x + 2 = 8
-2 -2

-2x = 6

And finally ...to solve for 'x' we need to divide both sides of the equation by -2....we do this because -2x divided by -2 = 1x right? also written as just x....so

-2x = 6
--------
-2 -2

x = -3

And that is your walk through :)