How do you solve #abs(x2)>x+4#?
The solution is
This is solving an inequality with absolute values.
There is no solution in the interval.
graph{x2x4 [18.01, 18.02, 9, 9.01]}
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To solve the inequality (x2 > x+4), you need to consider two cases:

When (x2) is nonnegative ((x \geq 2)): In this case, the absolute value (x2) is equal to (x2). So the inequality becomes: (x  2 > x + 4) Simplifying, we get: (2 > 4)
This is a contradiction, which means there are no solutions in this case.

When (x2) is negative ((x < 2)): In this case, the absolute value (x2) is equal to ((x2)), which is (x+2). So the inequality becomes: (x + 2 > x + 4) Simplifying, we get: (2 > 2x + 4) (2 > 2x) (1 > x)
Therefore, the solution to the inequality is (x < 1).
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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