Question

The problem is in the picture. Please help. I am reviewing for the SAT.

Answer 1

The absolute value of a quantity is 5 if that quantity is either 5 or -5.

So, the two solutions are

`2x+1=5 \iff 2x=4 \iff x=2`

`2x+1=-5 \iff 2x=-6 \iff x=-3`

Now, there is a bit of ambiguity here: we are not told who
`a` and
`b` are exactly, and yet the value of
`a-b` depends on our choice.

If we choose a = 2 and b = -3, then the value of a-b is 5

If we choose a = -3 and b = 2, then the value of a-b is -5

Answer 2

5

Explanation:

The solutions are the solutions to the two equations ...

• -5 = 2x +1 ⇒ x = -3
• 5 = 2x +1 ⇒ x = 2

The difference between the solutions is 5.

_____

If you consider what the absolute value is doing, it is telling you twice the difference between x and -1/2 is 5:

|2(x -(-1/2)}| = 5

|x -(-1/2)| = 5/2

The solutions to this will be points on the number line that are 5/2 units either side of -1/2, so they will be 5 units apart.

Effectively, the answer to the question is 2(5/2) = 5, where 5 is the number on the right of the equation, and the 2 in the denominator is the coefficient of x.

The 2 in the numerator comes from the solutions being separated by twice the distance either solution is from x=-1/2.