Solve for x |x|>5

Problem

|x|>5

Solution

1. Identify the type of inequality. The expression |x|>a (where a>0 represents the distance from x to the origin being greater than a units.

2. Apply the rule for absolute value inequalities involving the "greater than" symbol. The inequality |x|>a is equivalent to the compound inequality x>a or x<−a

3. Substitute the value 5 into the rule to find the specific intervals for x

4. State the solution in terms of the two separate inequalities or as an interval.

Final Answer

|x|>5⇔x<−5* or *x>5

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