Absolute value problem! Help please asap :) ...pleassseee help meee

Solve the following equation for all values of x: abs.(x+3)-9=2x

(All answers must check, and absolute value problems have 2 answers.)






Please show work and explain how you got about to your answer. Thanks for all you effort to help me i really appriciate your help.

Just so you know the mathematical symbol for ABS is | |. All you do is hold down the shift button and then push the \ button. It will make those straight parallel lines for you.

|x + 3| - 9 = 2x; add 9 to both sides
|x + 3| - 9 + 9 = 2x + 9; simplify
|x + 3| = 2x + 9; remove ABS bars
x + 3 = 2x + 9; subtract 2x from both sides
x - 2x + 3 = 2x - 2x + 9; simplify
-x + 3 = 9; subtract 3 from both sides
-x + 3 - 3 = 9 - 3; simplify
-x = 6; times both sides by -1
-x(-1) = 6(-1); solve
x = -6 <----------First answer

-|x + 3| - 9 = 2x; remove ABS bars and use parenthesis
-(x + 3) - 9 = 2x; distribute the - sign
-x - 3 - 9 = 2x; combine like terms
-x -12 = 2x; add 12 to both sides
-x - 12 + 12 = 2x + 12; simplify
-x = 2x + 12; subtract 2x from both sides
-x - 2x = 2x - 2x + 12; simplify
-3x = 12; divide both terms by -3
-3x/-3 = 12/-3; solve
x = -4 <----------Correct Answer

Check:
|-6 + 3| - 9 = 2(-6)?
|-3| - 9 = -12?
3 - 9 = -12?
-6 ≠ -12; doesn't check

|-4 + 3| - 9 = 2(-4)?
|-1| - 9 = -8?
1 - 9 = -8?
-8 = -8; it checks

Blessings

the expression x+3 cancels out at x=-3. For all values less than -3, x+3 is negative, and for all values greater than -3, x+3 is positive. So we can solve the equality for different intervals

For the interval x<-3

-(x+3)-9=2x
-x-3-9=2x
-x-12=2x
-12=3x
x=-4

For the interval x>-3

x+3-9=2x
x-6=2x
-6=x

Therefore, there are two solutions x=-4 and x=-6. However, the solution x=-6 is for the interval x>-3. Since -6 is not greater than -3, this solution does not exist, so the final ultimate super solution is x=-4