Which of the following is true if -3

Question

Which of the following is true if -34 E. |x-3|>5

niks18 · Accepted Answer

-3<x<9 , add both sides of the inequality  -3

=> -6<x-3<6

or  |x-3|<6

Option  C

generis · Answer

1) Find the distance between, then the midpoint of, the endpoints: 
 9 -(-3) = 12 
 \frac{12}{2} =  6  = midpoint

2) Change the inequality so it relates to 6 and -6. Subtract 3 from each side:
(-3 - 3) < x < (9 - 3)
-6 < x < 6

3) The -3 becomes part of the absolute value expression:
-6 < |x - 3| < 6, or
|x - 3| < 6

The last step just takes the two cases created by the absolute value inequality |x - 3| < 6, and combines them.

That is, -6 < |x - 3| < 6 says "the absolute value of something is less than 6 (and absolute value is nonnegative)," so change it to
|x - 3| < 6

To check: The two cases for |x - 3| < 6 are

LHS: x - 3 > - 6
RHS: x - 3 < 6
Combined: 
-6 < x - 3 < 6
-3 < x < 9 = original. Correct

Answer C

MathRevolution · Answer

=>

|x-a|<b 
⟺ -b < x – a < b 
⟺ a - b < x < a + b 
So, a is the midpoint of the end points a – b and a + b, and 
b is half the distance between the end points a – b and a + b.

The midpoint of -3 and 9 is  \frac{ }{2} = \frac{6}{2} = 3 . So,  a = 3 .
Since the distance between -3 and 9 is 12,  b = \frac{12}{2} = 6 .
Thus, |x-3| < 6.

Therefore, the answer is C.

Answer: C

AkshdeepS · Answer

You can use estimate here:

Add the ranges given and divide by 2 i.e., (9 + 3)/ 2 = 6
 
Only answer choice which has 6 at RHS is (C).

This method will work if we have all different number at RHS of inequality, but you can certainly narrow down your choices by this method.

Regular method is to Use POE and eliminate every answer choices.

jack0997 · Answer

Since this is not a MUST BE TRUE question, option A: –1 < x < 7 is also correct as this is within  -3<x<9 . It is correct to conclude?

Bunuel · Answer

Is true = must be true. If  -3< x < 9 , then  |x-3|<4  (-1<x<7) is not always true because if x is from -3 to -1, say if x = -2, or from 7 to 9, say of x = 8, then  |x-3|<4  will not be true.

Omnoui · Answer

The correct answer is C because |x−3|<6 --> -6 -3

Bro102 · Answer

There are also a way we choose x=-3 and x=9 then put these values in |x-3|
1st x=-3
 |-3-3| = |-6| = 6
2nd x=9 
 |9-3| = 6
 so 0<x<6
 ANS:C

Which of the following is true if -3<x<9?

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