Question

Which number line shows the solution set for |p-3|=9?

Answer 1

Answer:

Option b

$p = -6$ or $p = 12$

Step-by-step explanation:

The absolute value is a function that transforms any value x into a positive number.

Therefore, for the function $f(x) = |x|$  x> 0 for all real numbers.

Then the equation:

$|p-3| = 9$ has two cases

$(p-3) = 9$    if $h > 3$  (i)

$-(p-3) = 9$    if $h < 3$ (ii)

We solve the case (i)

$p = 9 + 3\\p = 12$

We solve the case (ii)

$-p +3 = 9\\p = 3-9\\p = -6$

Then the solution is:

$p = -6$ or $p = 12$