Solve the following inequality. Write the answer in interval notation. Note: If

Question

Solve the following inequality. Write the answer in interval notation. Note: If the answer includes more than one interval write the intervals separated by the "union" symbol, U.
4|x+7|-3 < 8

and another is:

|2x-6| is less than or equal to 13

Thanks!

Explanation / Answer

First, we want to understand absolute value |x+7| = x + 7 when x > 0 |x+7| = -x + 7 when x < 0 So, this means we are going to have two equations. Let x > 0, 4|x+7|-3 < 8 = 4(x+7) -3 < 8 = 4x + 28 - 3 < 8 = 4x + 25 < 8 = 4x < -17 = x < -(17/4) Let x < 0, 4|x+7|-3 < 8 = 4((-x)+7)-3 < 8 = -4x + 28 -3 < 8 = -4x < -17 = x > 17/4 Thus the interval is (in set builder notation) { x : x < -(17/4) U x > 17/4} and in interval notation (-inf, -17/4) U (17/4, inf) where inf = infinity. |2x-6|

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