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How do you graph and solve #|x-4|-5 <1#?

Answer 1

Mark the ends of the closed interval # [-2, 10]#. The segment in-between (sans the ends) is the graph for the inequality that is equivalent to #x> -2 and x<10#.

#|x-2|<6#.

This represents the couple's combined inequality.

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Answer 2

Jace Anderson

To graph and solve the inequality |x - 4| - 5 < 1, first, add 5 to both sides to isolate the absolute value term. This gives |x - 4| < 6. Then, split the inequality into two cases: 1. x - 4 < 6 2. -(x - 4) < 6 Solve each case separately to find the solution set. For the first case, add 4 to both sides to get x < 10. For the second case, subtract 4 from both sides and negate the inequality to get x > -2. Combine both solution sets to get the final solution: -2 < x < 10. To graph the solution on a number line, plot an open circle at -2 and another open circle at 10, then shade the region between them.

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Answer from HIX Tutor

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.

How do you graph and solve #|x-4|-5 &lt;1#?

How do you graph and solve #|x-4|-5 <1#?