Question

Saw the following absolute value equations if you need it right answer as a fraction reduced to lowest terms

Answer 1

The equation given is,

`\left|6x-10\:\right|=\left|5x+6\right|`

Find the positive and the negative intervals

`x<-(6)/(5),\:\:-(6)/(5)\le \:x<(5)/(3),\:\:x\ge (5)/(3)`

Solve the inequality for each intervals

`\begin{gathered} \mathrm{No\:Solution}\quad \mathrm{or}\quad \:x=(4)/(11)\quad \mathrm{or}\quad \:x=16 \\ x=(4)/(11)\quad \mathrm{or}\quad \:x=16 \end{gathered}`

Hence, the answer is

`x=(4)/(11)\quad\mathrm{or}\quad\:x=16\text{ \lparen Two solutions\rparen}`