Question 346651: When solving the problem |X + 3| + 8 > 4 do you go to |x + 3|> -4 which has no solution or to x + 3 + 8> 4 and -x -3 + 8>4?
Answer by CharlesG2(834)   (Show Source):
You can put this solution on YOUR website! When solving the problem |X + 3| + 8 > 4 do you go to |x + 3|> -4 which has no solution or to x + 3 + 8> 4 and -x -3 + 8>4?
|x + 3| + 8 > 4
|x + 3| > -4 (subtracted 8 from both sides)
(comment here added after posting earlier-->
notice it is |x + 3| > -4, all values for |x + 3| are gonna be greater than a negative number, now if it were |x + 3| < -4 now that would have no solution, an absolute value can not be less than a negative number)
x + 3 < 4 OR x + 3 > - 4
subtract 3 from both sides in both
x < 1 OR x > -7 --> all values of x work
so no not no solutions, since all values of x work
if I plug in a negative number for x, it would be a positive number plus 8, and that would be greater than 4
if I plug in a positive number for x, result would be greater than 4
if I plug in 0 (zero) for x, result would be greater than 4
these 2 problems: x + 3 + 8> 4 and -x -3 + 8>4
x + 11 > 4 and -x + 5 > 4
x > -7 and -x > -1
x > -7 and x < 1
yes that would be same result
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