Question

What are the solution intervals for |x – 4| – 2 > 7?

A. x > –5 and x < 13

B. x < –5 or x > 13

C. x > 5 or x < –13

D. x < 5 and x > –13

Answer 1

ok, first move the -2 to the right hand side by adding 2 to both sides. what do you end up with?

Answer 2

x - 4 > 9

Answer 3

almost, it should be:

|x-4| > 9

Answer 4

next - do you know what the "|" symbols around a number mean?

Answer 5

isnt it absolute value?

Answer 6

yes - and that in turn means ignore the sign of the result - just look at its magnitude

Answer 7

so you can break this equation up into two cases:

1. x - 4 > 9
2. -(x - 4) > 9

agreed?

Answer 8

yes

Answer 9

so solve each one - what do you end up with?

Answer 10

x > 13
x < 13

Answer 11

you have the first one correct

Answer 12

for the second one we have:

-(x - 4) > 9 which leads to:
-x + 4 > 9 try and solve from here

Answer 13

x < 5

Answer 14

almost...

Answer 15

we get:

-x + 4 > 9 therefore:
-x > 5 then multiply both sides by -1 (which also swaps the inequality sign)
x < -5

Answer 16

I hope that makes sense

Answer 17

yes i understand

Answer 18

great!

Answer 19

thank you so much

Answer 20

yw :)