Question

Which compound sentence is equivalent to |x - 5| < 4?

A. x - 5 > 4 or x - 5 < -4
B. -4 < x - 5 < 4
C. -8 < 2x + 3 < 8
D. x - 5 = 4 or x - 5 = -4
E. 2x + 3 > 8 or 2x + 3 < -8

Answer 1

Look at it on a number line. Whatever x-5 equates to, you will change the sign to be positive (that's taking the absolute value). So, obviously, if x-5 is positive, it will be to the left (towards 0) of 4. If x-5 is negative, it will be to the right (again, towards 0) of -4.

So the answer will lie somewhere between -4 and 4. Which answer corresponds to this?

Note: The reason we went towards 0 in both cases is because you are < 4. If you were > 4, we'd have gone *away* from 0.

Answer 2

ok i get what you saying so.... i think its A

Answer 3

x-5 > 4 is going *away* from 0...not towards. SInce both are going towards 0, they'll meet at 0 and you'll get one combined interval.

Look at them again. ;)

Answer 4

ok. so of there going away from zero then there negative.... so hmmm.. *thinking*

Answer 5

Ok...let me try this a different way. To say that an number is to the "left of 4" means that it is < 4. To say that a number is to the "right of -4" means that it is > -4.

So which of those has that x-5 must be both < 4 and > -4?

Answer 6

OH :D its d!

Answer 7

Wait...not quite.

Answer 8

b kinda looks the same... so is that it?

Answer 9

You don't want it to be equal to 4...you want x-5 < 4 and x-5 > -4. You want x-5 to be between -4 and 4.

We've elliminated A and D from my responses, and C and E make no sense (where did 2x+3 come from?). What does that leave you?

Answer 10

Exactly. B says that x-5 < 4 and x-5 > -4.

Just like if you had two equations, say, y=3x+4 and y=2x-3, you can combine these by merging the y's and gettign 2x-3=3x+4...same holds true with inequalities.

The only difference, is you have to make sure you pivot the equation onthe inequality sign...by that I mean that x-5 > -4 becomes -4 < x-5.

Then when you put them together you have -4 < x-5 < 4.

Understand better?

Answer 11

yes i do thankyou :)... i think i have another one... can you help me on that?

Answer 12

Sure. :)