SOLUTION: find all of the possible solutions for x that satisfy the following inequality |-(x+2)^2 +1| greater than or equal to 1.

Question 214460: find all of the possible solutions for x that satisfy the following inequality |-(x+2)^2 +1| greater than or equal to 1.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
|-(x+2)^2 +1| greater than or equal to 1
-1 <= -(x+2)^2+1 <= 1
Subtract 1 along the line to get:
-2 <= -(x+2)^2 <= 0
---
Multiply thru by -1 to get:
0 <= (x+2)^2 <= 2
---
Take the square root along the line to get:
0 <= x+2 <= sqrt(2)
---
Subtract 2 along the line to get:
-2 <= x <= sqrt(2)-2
============================
Cheers,
Stan H.

RELATED QUESTIONS
which of the following describes all the values of x that satisfy 5-2(3-x)>_5x-3(x-1)? (answered by jim_thompson5910)

Solve the inequality, and express the solutions in terms of intervals whenever possible. (answered by lwsshak3)

Find all the possible real numbers of x that satisfy the inequality: x-1/x+2 >2 *I... (answered by richwmiller)

Find X values that satisfy the following inequality: X^2+1 > 0. Show your... (answered by josgarithmetic)

Find X values that satisfy the following inequality: X^2+3X+1 >... (answered by josgarithmetic)

Solve the following equations and inequality for x. If the solution is extraneous, please (answered by josgarithmetic)

the number of integers x that satisfy the following inequality X^2 - 5x + 1 =0... (answered by josgarithmetic)

find all values of in the interval 0 2π that satisfy the inequality sin... (answered by lynnlo)

Find all values of theta that satisfy the condition sin theta < -1 where 0 degrees <_... (answered by stanbon,Edwin McCravy)