Math for extra credit

Question

If a and b are the solution to the equation below what is the value of |a - b|

|2x + 1| - 3 = 2

Answer 1

Hi,

|2x + 1| - 3 = 2

Before solving, you need to know the meaning of absolute value: | X | = K , K>0 always you have

X = ± K

Now |2x + 1| - 3 = 2 -----> |2x + 1| = 5 compare with above then you have:

2x + 1 = ±5------> 2x + 1 = 5---------> x = 2 and another solution will be

2x + 1 = -5--------> x = -3

now replace to the a = -3, b = 2 |a - b| = |-3 - 2 | = 5 OR a = 2, b = -3 |2 -(-3) | = 5

it is not important, you choose which number is a or b, anyway you have the same answer

I hope it is useful.

Minoo

Answer 2

Hi, if |x| = a then x=a or x=-a.

Therefore, we first have to isolate the absolute value. So add both sides by 3. We get,

|2x+1| = 5

Therefore, 2x+1 = 5 OR 2x+1 = -5

2x = 4 2x = -6

x = 2 x = -3

Therefore our two solutions are 2 and -3.

|a - b| = |2 - (-3)| = |2+3| = |5| = 5.

Hope it helps.