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

Good luck on your assignment and enjoy your day

`\frak{LoveYourselfFirst:)}`

Answer 2

A

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