Expert: Scott A Wilson - 6/17/2010

Question
i need help with the following

7x - 2 = 6x + 4

4x + 7 + 3x = 5x + 13 + x

2/3 x =6

4x - 2 + 7 = 36

3x/4 + 2/3 = 2x/3 - 2

Answer
7x - 2 = 6x + 4
Add 2-6x to both sides.
7x - 2 + 2 - 6x turns into x since -2+2 = 0 and 7x-6x=1x=x.
6x + 4 + 2 - 6x turns into 6 since 4+2=6 and 6x-6x=0.
The left side is x, the right side is 6, so the answer is x=6.
Understanding this, do this to the rest of the problems.

4x + 7 + 3x = 5x + 13 + x
This combine first to 7x + 7 = 6x + 13, right?
Then add -6x-7 to both sides, and that gives x = 6, right?

2/3 x =6
Multiply both sides by 3/2, giving x=9, right?

4x - 2 + 7 = 36
Take 7, subtract 2, and get a number.
Subtract that number from both sides, giving 4x = 36 - that number.
Divide both sides by 4, giving x = so many fourths.

3x/4 + 2/3 = 2x/3 - 2
I find it easiest to eliminate fractions.
Since both 3 and 4 go into 12, multiply the whole equation by 12.
This should be 9x + 8 = 8x - 24, right?
You can subtract 8x from both sides and 8 from both sides, giving a value for x.

After doing math for this many years, I find it cuts down on my errors to always think of subtracting as adding a negative.  This means I think of it as adding -8 - 8x to both sides.