Question

Describe all the x-values within or including a distance of the given value. (Enter your answer using interval notation.)Distance of 10 units from the number 3

Answer 1

The value of x that has 10 units from the number is 3 is :

$\lvert x-3\rvert=10$

An absolute value has positive and negative signs, this will be :

$\begin{gathered} x-3=10 \\ x=10+3 \\ x=13 \end{gathered}$

and

$\begin{gathered} x-3=-10 \\ x=-10+3 \\ x=-7 \end{gathered}$

The answer is x = -7 and 13