Question

How do you solve `|x+2|= 4`?

Answer 1

`x=-6color(white)("XX")orcolor(white)("XX")x=2`

Explanation:

Consider the two possibilities:
#{: (x+2 < 0,color(white)("XX")andcolor(white)("XX"),x+2 > 0), (rarr abs(x+2) = -x-2,,rarrabs(x+2)=x+2), ("so "abs(x+2)=4,,"so "abs(x+2)=4), (rarr -x-2 =4,,rarr x+2=4), (rarr -x=6,,rarrx==2), (rarr x=-6,,) :}#

Answer 2

`x=2" or " x=-6`

Explanation:

Equations with an`color(blue)" absolute value"` normally have 2 solutions.

These are found by solving `x+2=color(red)(+-)4`

`color(blue)"Solution 1"`

`"solve "x+2=4rArrx=4-2=2`

`color(blue)"Solution 2"`

`"solve " x+2=-4rArrx=-4-2=-6`

`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=2to|2+2|=|4|=4=" right side"`

`x=-6to|-6+2|=|-4|=4=" right side"`

`rArrx=2" or "x=-6" are the solutions"`