What are all values of x for which |x - 2| < 3?
Explanation on how to get the answer
this is question 17 for the 2nd test for the Math level 1 of the official SAT college board blue book for mathematics level 1 & level 2
SAT math level 1 test 2 blue book question?
2016-12-20 11:20 am
回答 (2)
2016-12-20 11:40 am
✔ 最佳答案
|x - 2| < 3±(x-2) < 3
We have (x-2) < 3
x < 5
and
-(x-2) < 3
x-2>-3
x>-1
Solution : -1<x<5
2016-12-20 11:35 am
You need to know that |a| < b is equivalent to -b < a < b
So |x - 2| < 3 is equivalent to -3 < x - 2 < 3, that is -3 < x - 2 and x - 2 < 3
In each inequality you can add 2 to both sides:
-1 < x and x < 5, that is -1 < x < 5.
And that is the answer to the question.
Edit: You should also know the rule that |a| > b is equivalent to "a > b or a < -b".
So |x - 2| < 3 is equivalent to -3 < x - 2 < 3, that is -3 < x - 2 and x - 2 < 3
In each inequality you can add 2 to both sides:
-1 < x and x < 5, that is -1 < x < 5.
And that is the answer to the question.
Edit: You should also know the rule that |a| > b is equivalent to "a > b or a < -b".
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