# Match the inequalities with the corresponding statements.

1. Jun 30, 2011

### name_ask17

1. The problem statement, all variables and given/known data

PROBLEM: Match the inequalities with the corresponding statements.
INEQUALITIES: 1) |a-5|< 1/3
2) |a- 1/3|< 5
STATEMENTS: a) The distance from a to 5 is less than 1/3
b) a is less than 5 units from 1/3

3. The attempt at a solution

I solved for a for both problems and for both problems I am getting 14/3 < a< 16/3.
My problem is that since I am getting the same solution for both problems, then aren't both the statements (a and b) correct for both of the inequalities? Or am I getting the wrong answers when I solve the inequalities? Please advise if you see the problem. Thanks in advance.

2. Jun 30, 2011

### vela

Staff Emeritus
It seems you've solved the inequalities incorrectly, but solving them really isn't necessary. You want to be able to interpret the inequalities as written. For example, what does |a-5| correspond to geometrically?

3. Jun 30, 2011

### SammyS

Staff Emeritus
Of course, vela is correct, but if you want to check what's wrong with your algebraic method, show how you get the answer for each inequality.

4. Jun 30, 2011

### name_ask17

VELA: Geometrically, |a-5| corresponds to moving a over right 5, correct? But how does that help me interpret the inequality as written? Or am I interpreting it incorrecly. Please advise.

SAMMY: This is how I worked the first one out algebraically.
|a-5|< 1/3 has two solutions right? One positive and one negative?
Solution 1:
a-5 < 1/3
a< 1/3 + 5
a < 16/3

and a-5 > -1/3
a > -1/3 + 5
a > 14/3

So that gives me 14/3 < a< 16/3.
And I worked out the second problem with the same steps to get the same answer. I'm confused.

5. Jun 30, 2011

### ehild

You made a mistake:
|a-1/3|<5 means -5<a-1/3<5. Adding 5 to all sides, you get a negative number on the left. You just missed that minus sign.

ehild

6. Jun 30, 2011

### Staff: Mentor

No, |a - 5| represents the distance between a and 5. Looking at things in terms of transformations, which you seem to be doing, the graph of y = |x - 5| can be seen as the translation of the graph of y = |x| by 5 units to the right.

7. Jun 30, 2011

### vela

Staff Emeritus
No. |a-5| is equal to the distance between a and 5. For example, when a=4 which is a distance of 1 away from 5 on the number line, you get |a-5|=1. Similarly, a=6.5, which is 1.5 more than 5, you get |a-5|=1.5.

So if you had an inequality like |x-1| < 2, you can interpret that as

Code (Text):
|x-1|  =  "the distance between [i]x[/i] and 1"
<    =  "is less than"
2    =  "two"

8. Jun 30, 2011

### name_ask17

ahh. just what i needed. thanks to all(:

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