SAT Question

Rank: Hard

Topic: Algebra, Equations, Absolute Values

Below is a question from a recent SAT exam. It is a non-calculator question that would typically take a student 2-3 minutes to complete.

|2x+1|=5

If a and b are soloutions to the equation above, what is the value of |a-b|?

As we are working with an absolute value we can split this equation into two equations. One equal to positive 5 and the other equal to negative 5.

Firstly,

2x+1=5

And,

2x+1=-5

Now we will call the soloution to the first equation a and the soloution to the second equation b.

2a+1=5 and 2b+1=-5

Solving these equation gives us,

2a=4  and 2b=-6

a=2 and b=-3

Now we must find the value of |a-b|

So we substitute in the values of a and b.

|2--3|=|5|=5

Therefore, the answer is 5.