Question

Which number line shows the solution set for |y-9| <12

Answer 1

Answer:

Option c

$y\geq-3$ or $y \leq 21$

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 inequation:

$|y-9| \leq 12$ has two cases

$(y-9)$    if $y \geq 9$  (i)

$-(y-9)$    if $y < 9$ (ii)

We solve the case (i)

$y \leq 9 + 12\\y\leq21$

We solve the case (ii)

$-y +9 \leq 12\\-y \leq 12-9\\y \geq -3$

Then the solution is:

$y\geq-3$ or $y \leq 21$