Question

Which of the number line graphs shows the soulution set of |x-2| >3?​

Answer 1

Hey there!

$\boxed{\boxed{\bold{Answer:A}}}$ $\bold{\checkmark}$

There's actually $\bold{two}$ possibilities in  this particular $\bold{equation}$

                                                                             1.

• $\bold{x-2>3}$
• $\bold{Add}$ by $\bold{2}$ on each of your sides
• $\bold{x-2+2>3+2}$
• $\bold{Cancel:-2+2}$
• $\bold{Keep:3+2}$

• $\bold{3+2=5}$
• $\boxed{\bold{x>5}}$

                                                                               2.

• $\bold{x-2$
• $\bold{Add}$ by $\bold{2}$ on each of your sides (again)
• $\bold{x-2+2$
• $\bold{Cancel:-2+2}$
• $\bold{Keep:-3+2}$
• $\bold{-3+2=-1}$
• $\boxed{\bold{x$

Good luck on your assignment and enjoy your day

$\frak{LoveYourselfFirst:)}$

Answer 2

Answer:

A

Step-by-step explanation:

There are 2 solutions with absolute value equations

x-2 >3       or    x-2 <-3

Add 2 to each side

x-2+2>3+2   or     x-2+2 <-3+2

x>5               or       x <-1

x< -1  or x>5

This looks like boat oars

Open circle at -1  and to the left

Open circle at 5 and to the right