Question

/5×+4/ =/×+9/ solve for x​

Answer 1

`\large\boxed{x=(5)/(4)\ \vee\ x=-(13)/(6)}`

Explanation:

`|5x+4|=|x+9|\iff5x+4=x+9\ or\ 5x+4=-(x+9)\\\\5x+4=x+9\qquad\text{subtract 4 from both sides}\\5x=x+5\qquad\text{subtract x from both sides}\\4x=5\qquad\text{divide both sides by 4}\\x=(5)/(4)\\\\5x+4=-(x+9)\\5x+4=-x-9\qquad\text{subtract 4 from both sides}\\5x=-x-13\qquad\text{add x to both sides}\\6x=-13\qquad\text{divide both sides by 6}\\x=-(13)/(6)`