We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

#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