# Why do I keep getting this wrong?

• Apr 1st 2008, 03:06 AM
Coach
Why do I keep getting this wrong?
The problem

3x-(1+2x)=6 Please pretend the parenthesis are aboslute value bars

my solution

$-(1+2x)=-6+3x$divide both sides by -1

$(1+2x)=6-3x$

$1+2x=6-3x$ or $1+2x=-6-3x$

x= 1 or x=7, but only seven is valid in the original equation. Why?

Thank you in advance!
• Apr 1st 2008, 03:15 AM
mr fantastic
Quote:

Originally Posted by Coach
The problem

3x-(1+2x)=6 Please pretend the parenthesis are aboslute value bars

my solution

$-(1+2x)=-6+3x$divide both sides by -1

$(1+2x)=6-3x$

$1+2x=6-3x$ or $1+2x=-6-3x$

x= 1 or x=7, but only seven is valid in the original equation. Why?

Thank you in advance!

|1 + 2x| = 3x - 6.

Note that:
1. |1 + 2x| = 1 + 2x when 1 + 2x > 0 => x > -1/2.
2. |1 + 2x| = -(1 + 2x) = -1 - 2x when 1 + 2x < 0 => x < -1/2.

1. 1 + 2x = 3x - 6 AND x > -1/2 => x = 7 AND x > -1/2 => x = 7.

2. -1 - 2x = 3x - 6 AND x < -1/2 => x = 1 AND x < -1/2 => no solution.

So x = 7 is the only solution.