Question 637463: absolute value of (4x + 2) is less than or equal to 14
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! Solve for domain of x that satisfies abs(4x+2) <= 14
The "trick" here is to use the DrBeeee identity for absolute value.
If y > 0, then abs(y) = y
If y < 0, then abs(y) = -y
Apply my identity to your problem;
If (4x+2)>0 then abs(4x+2) = 4x+2
solve 4x+2 > 0 gives x > -1/2 and
4x+2 <= 14 gives x <= 3
If (4x+2) < 0 then abs(4x+2) = -(4x+2)
solve 4x+2 < 0 gives x < -1/2 and
-(4x+2) <= 14 gives x >= -3
Thus the solution domain for x is
-3 <= x <= 3
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