Question

Describe all numbers x that are at a distance of 1 from the number 8 . Express this using absolute value notation. The answer field below uses the symbol mode option in Mobius. That lets you type in a vertical bar | to represent absolute values. Also, when you type in < and then = , the symbol mode will automatically convert that to ≤ . In the same way, if you type in > and then = , the symbol mode will automatically convert that to ≥ .

Answer 1

To solve this, let's think about what are the numbers that are at a distance of 1 from 8. We can take 8 and:

`\begin{gathered} 8+1=9 \\ . \\ 8-1=7 \end{gathered}`

Those are the only two numbers that verify the asked. Now we need to express it using absolute value notation. If two numbers are at a certain 'distance', this means that their difference is that 'distance'. Since we want the distance between a number x and 8 to be 1, we can write:

`\begin{gathered} x-8=\pm1 \\ \\ \end{gathered}`

Because:

`\begin{gathered} 7-8=-1 \\ . \\ 9-8=1 \end{gathered}`

And we can write this plus-minus sign using absolute value:

`|x-8|=1`

Thus, the answer is:

`|x-8|=1`