Question

How do you solve `3| x + 9| - 6= 24`?

Answer 1

The solutions are `S={1, -19}`

Explanation:

This is an equation with absolute values.

`3|x+9|-6=24`

`=>`, `3|x+9|=24+6=30`

`=>`, `|x+9|=10`

Therefore,

`{(x+9=10),(-x-9=10):}`

`<=>`, `{(x=10-9=1),(x=-9-10=-19):}`

The solutions are `S={1, -19}`

graph{3|x+9|-30 [-35.5, 29.47, -20.1, 12.38]}

Answer 2

`x=-19" or "x=1`

Explanation:

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

`"add 6 to both sides and divide by 3"`

`3|x+9|=24+6=30`

`|x+9|=30/3=10`

`color(magenta)"positive expression"`

`x+9=10`

`"subtract 9 from both sides"`

`x=10-9=1`

`color(magenta)"negative expression"`

`-(x+9)=10`

`-x-9=10`

`"add 9 to both sides"`

`-x=10+9=19rArrx=-19`

`color(blue)"As a check"`

Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

`x=1`

`3|10|-6=(3xx10)-6=30-6=24`

`x=-19`

`3|-10|-6=30-6=24`

`x=-19" or "x=1" are the solutions"`