Question

Im having trouble solving this absolute value equation. can someone help me out? −2∣5w−7∣+9=−7

Answer 1

`-2\big|5w-7\big|+9=-7\quad|-9\\\\-2\big|5w-7\big|=-7-9\\\\-2\big|5w-7\big|=-16\quad|:(-2)\\\\\big|5w-7\big|=8`

so


`5w-7=8\qquad\vee\qquad5w-7=-8\\\\ 5w-7=8\quad|+7\qquad\vee\qquad5w-7=-8\quad|+7\\\\ 5w=8+7\qquad\vee\qquad5w=-8+7\\\\ 5w=15\quad|:5\qquad\vee\qquad5w=-1\quad|:5\\\\ \boxed{w=3\qquad\vee\qquad w=-(1)/(5)}`

Answer 2

Are there any options?