# How do you solve the inequality #abs(1-2x)>=x+5# and write your answer in interval notation?

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To solve the inequality (|1 - 2x| \geq x + 5), we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.

Case 1: (1 - 2x \geq x + 5) (1 - 2x - x \geq 5) (-3x \geq 4) (x \leq -\frac{4}{3})

Case 2: (1 - 2x \leq -(x + 5)) (1 - 2x \leq -x - 5) (-2x + x \leq -1 - 5) (-x \leq -6) (x \geq 6)

Combining both cases, we have (x \leq -\frac{4}{3}) or (x \geq 6).

In interval notation, this solution is ((-∞, -\frac{4}{3}] \cup [6, ∞)).

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When evaluating a one-sided 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 one-sided 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 one-sided 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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