Question

So I did #67 and I got -8(correct) but I’m trying to figure out how people were able to get the other answer which is 6/5

Answer 1

We can divide both sides by the expression on either side:

`|3x+1|=|2x-7|\implies(|3x+1|)/(|2x-7|)=1\implies\left|(3x+1)/(2x-7)\right|=1`

Then we use the definition of absolute value:

`|x|:=\begin{cases}x&\text{if }x\ge0\\-x&\text{if }x<0\end{cases}`

So we have two possible cases:

1) If
`(3x+1)/(2x-7)\ge0`, then
`\left|(3x+1)/(2x-7)\right|=(3x+1)/(2x-7)`, and solving the equation gives

`(3x+1)/(2x-7)=1\implies3x+1=2x-7\implies x=-8`

2) If
`(3x+1)/(2x-7)<0`, then
`\left|(3x+1)/(2x-7)\right|=-(3x+1)/(2x-7)`, and

`-(3x+1)/(2x-7)=1\implies(3x+1)/(2x-7)=-1\implies3x+1=-2x+7\implies5x=6`

`\implies x=\frac65`