Question

How do you solve `- 5| x + 1| = -10`?

Answer 1

`x=1" or "x=-3`

Explanation:

`"divide both sides by "-5`

`cancel(-5)/cancel(-5)|x+1|=(-10)/(-5)`

`rArr|x+1|=2`

`"the value inside the absolute value function can"`
`"be positive or negative"`

`"hence there are 2 possible solutions"`

`color(blue)"first solution"`

`x+1=2rArrx=2-1=1`

`color(blue)"second solution"`

`-(x+1)=2`

`rArr-x-1=2`

`rArr-x=2+1=3rArrx=-3`

`color(blue)"As a check"`

`x=1to-5|2|=-5xx2=-10larr"True"`

`x=-3to-5|-3+1|=-5|-2|==-10larr"True"`