Which inequality is equivalent to |x-4|<9?
A. –9 > x – 4 < 9
B. –9 < x – 4 < 9
C. x – 4 < –9 or x – 4 < 9
D. x – 4 > –9 or x – 4 < 9
I put B?
Are you asking us or telling us?
In any event, B is correct.
Haha asking, thank you Steve!
You are correct. The inequality equivalent to |x - 4| < 9 is B. –9 < x – 4 < 9.
To determine which inequality is equivalent to |x-4|<9, we need to understand what the absolute value represents.
The absolute value |x-4| is the distance between x and 4 on the number line. In other words, it measures how far x is from 4, regardless of whether it is to the left or right of 4.
Knowing this, we can analyze the options:
A. –9 > x – 4 < 9: This implies that x - 4 is between -9 and 9, but it does not consider the absolute value. It is not correct.
B. –9 < x – 4 < 9: This option states that x - 4 is between -9 and 9, which captures the condition that |x-4|<9. This means that x is within 9 units of 4 (either to the left or right). Therefore, B is the correct answer.
C. x – 4 < –9 or x – 4 < 9: This option states that x - 4 is either less than -9 or less than 9, which is not accurate. It implies that x can be both less than -9 and less than 9, which contradicts the condition given.
D. x – 4 > –9 or x – 4 < 9: This option states that x - 4 is either greater than -9 or less than 9, which doesn't accurately represent the condition |x-4|<9. It allows for values of x that are both larger than -9 and smaller than 9, which is incorrect.
Therefore, your answer choice of B is correct.