#2**+5 **

CPhill is correct - He's rarely wrong. I just want to look at it myself.

Think about this for a moment

$$|a|=|t|$$

This would be true if x=t and it would also be true if x=-t

The same thing applies to your question:

$$\begin{array}{rlll}

|3y+6|&=&|3y+3|\\

(3y+6)&=&\pm (3y+3)\quad &\mbox{now factorise both sides}\\

3(y+2)&=&\pm 3(y+1)\quad &\mbox{next divide both sides by 3}\\

y+2&=&\pm (y+1)

\end{array}$$

Now we seperate this into 2 equations

$$\begin{array}{rlllrl}

y+2&=&+(y+1)\quad &\mbox{and}\qquad y+2&=&-(y+1)\\

y+2&=&y+1\quad &\mbox{and}\qquad y+2&=&-y-1\\

y&=&y-1\quad &\mbox{and}\qquad 2y&=&-3\\

y&=&\mbox{no soln}\quad &\mbox{and}\qquad y&=&\frac{-3}{2}\\

\end{array}$$

So the answer is y=-1.5

Melody
Jun 1, 2014

#1**+5 **

I'm going to change the "y's" to "x's"

So we have

l3x+6l = l3x+3l

Factor a 3 out of each and we get

lx+2l = lx+1l

Take both things out of the absolute value bars. So we have

x+2 = x+1 and there's no solution to this

Now set x+2 = -(x+1) .......So we have

x+2 = -x -1 Add x to both sides

2x + 2 = -1 Subtract 2 from both sides

2x = -3 Divide by 2 on both sides

x = -3/2 = -1.5

Here's a graph of the solution:

P.S. ... You can back-substitute "y" for "x" if you'd like....

The leftmost function on the graph is l3x+6l and the rightmost is l3x+3l

You can back-substitute "y" for "x" if you'd like......

CPhill
May 30, 2014

#2**+5 **

Best Answer

CPhill is correct - He's rarely wrong. I just want to look at it myself.

Think about this for a moment

$$|a|=|t|$$

This would be true if x=t and it would also be true if x=-t

The same thing applies to your question:

$$\begin{array}{rlll}

|3y+6|&=&|3y+3|\\

(3y+6)&=&\pm (3y+3)\quad &\mbox{now factorise both sides}\\

3(y+2)&=&\pm 3(y+1)\quad &\mbox{next divide both sides by 3}\\

y+2&=&\pm (y+1)

\end{array}$$

Now we seperate this into 2 equations

$$\begin{array}{rlllrl}

y+2&=&+(y+1)\quad &\mbox{and}\qquad y+2&=&-(y+1)\\

y+2&=&y+1\quad &\mbox{and}\qquad y+2&=&-y-1\\

y&=&y-1\quad &\mbox{and}\qquad 2y&=&-3\\

y&=&\mbox{no soln}\quad &\mbox{and}\qquad y&=&\frac{-3}{2}\\

\end{array}$$

So the answer is y=-1.5

Melody
Jun 1, 2014