Question 233438: if you could can you please explain to me how to solve this math problem? thank you soooo much!! (:
(I stands for absolute value since i dont have the actual symbol)
I x I + 4 (is less than) 9
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! You can use the function term of abs(x) to indicate the absolute value of x.
Otherwise, it's the symbol above the backslash which is to the right of the letter P three keys to the right on my keyboard.
It looks like a broken line going straight up and down with a space in the middle. When you hit the key, it shows up as | which is not broken in the middle by a space.
Anyway .....................
abs(x) + 4 < 9
subtract 4 from both sides of this equation to get:
abs(x) < 9-4 which becomes abs(x) < 5
by definition, abs(x) < 5 means that:
x < 5 if x is positive.
-x < 5 if x is negative.
solve for x < 5 to get x < 5
take -x < 5 and multiply both sides of this equation by -1 to get:
x > -5
your answer is that x is either < 5 or x > -5
this can be written as -5 < x < 5
to prove, plug good and bad values of into the original equation to see what happens.
take x = -5,-4,0,4,5
x = -5,5 are outside of the limits so the answer should be false.
x = -4,0,4 are inside the limits so the answer should be true.
Let y = abs(x) + 4 < 9
when x = -5, y = 9 not < 9 so this is good because -5 is outside of the limits.
when x = -4, y = 8 < 9 so this is good because -5 is inside the limits.
when x = 0, y = 4 < 9 so this is good because 0 is inside the limits.
when x = 4, y = 8 < 9 so this is good because 4 is inside the limits.
when x = 5, y = 9 not < 9 so this is good because 5 is outside the limits.
Your answer is:
-5 < x < 5
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