Question

|7x+1|-|5x+6|=0

Answer 1

`|7x+1|-|5x+6|=0`

`<=> |7x+1|=|5x+6|`

\(\Leftrightarrow\left[{}\begin{matrix}7x+1=5x+6\\7x+1=-5x-6\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=-\dfrac{7}{12}\end{matrix}\right.\)

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Answer 2

   |7x+1| - |5x+6|=0

⇔ |7x+1| = |5x+6|

⇔\(\left[{}\begin{matrix}7x+1=5x+6 \\7x+1=-5x-6\end{matrix}\right.\) ⇔  \(\left[{}\begin{matrix}2x=5\\12x=-7\end{matrix}\right.\)

⇔\(\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=\dfrac{-7}{12}\end{matrix}\right.\)

Answer 3

\(\left|7x+1\right|-\left|5x+6\right|=0\) 

\(\Rightarrow\left|7x+1\right|=\left|5x+6\right|\) 

\(\Leftrightarrow\left[{}\begin{matrix}7x+1=5x+6\\7x+1=-5x-6\end{matrix}\right.\) 

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=\dfrac{-7}{12}\end{matrix}\right.\)