|2x+1|=5
If a and b are the solutions to the equation above, what is the value of |a-b| ?

Answer

5

Explanation

By definition of absolute value, if | 2x + 1 | = 5, then 2x + 1 = 5 or −(2x + 1) = 5, which can be rewritten as 2x + 1 = −5. Subtracting 1 from both sides of 2x + 1 = 5 and 2x + 1 = −5 yields 2x = 4 and 2x = −6, respectively. Dividing both sides of 2x = 4 and 2x = −6 by 2 yields x = 2 and x = −3, respectively. If a and b are the solutions to the given equation, then a = 2 and b = −3. It follows then that | a − b | = |2 − (−3) | = | 5 | , which is 5. Similarly, if a = −3 and b = 2, it follows that a − b = | −3 − 2 | = | −5 || | , which is also 5.