# Is 0 a positive value? (linear inequalities) Or is self-study book wrong?

##### New member
Hi there,

As those of you who kindly answered my previous posts will know, I'm self studying algebra from a book called 'Teach yourself algebra: a complete introduction.' Now, all of my previous posts have been concerning specific problems, this one however, is a bit more general. I've reached the section on 'linear inequalities' and am having few difficulties in understanding the material, on one little detail however, my book is being somewhat ambiguous.

For the simultaneous inequalities that I'm required to solve in the current exercise it is clearly stated 'Find the positive values of X which satisfy both the inequalities.'

Now the format of the book is such that before making you solve any specific kind of problem yourself you are always given a 'worked example.'

Now my problem is that in the 'worked example' for this kind of problem 0 is not included as a positive value. The answer is given 0<X<3. Unfortunately when I go on to solve the first of these problems in the following exercise, in the 'answers' section of the book 0 is included as a positive value. I am certain that I've solved the two simultaneous inequalities correctly and they are (solved) X<8 and X<5. Following the methodology of the 'worked example' therefore, I've given my answer as 0<X<5. Unfortunately when I flip to the 'answers' section of my book, the correct answer provided suggests that I should have included 0 as a positive value: 0<X<5.

Is is the book trying to tell me that both ways are correct and that 0 can be either considered as positive or not included at all? Or does the book contain an error here? In short, is 0 to be considered as a positive value or not in the solution of this kind of inequality problem?

My Google searches have done little to clarify the situation. They tell me that in the English speaking world 0 is considered as neither positive nor negative, but that in the minds of the French 0 can be either positive or negative.

Any clarification on this matter would be much appreciated.

Many thanks,
Tom.

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#### Otis

##### Senior Member
Looks like a book error. Your answer is correct. Zero is neither positive nor negative, unless defined as such for the purpose at hand. (Eg: electrical engineers sometimes define zero as negative because it makes things easier.)

#### JeffM

##### Elite Member
Hi there,

As those of you who kindly answered my previous posts will know, I'm self studying algebra from a book called 'Teach yourself algebra: a complete introduction.' Now, all of my previous posts have been concerning specific problems, this one however, is a bit more general. I've reached the section on 'linear inequalities' and am having few difficulties in understanding the material, on one little detail however, my book is being somewhat ambiguous.

For the simultaneous inequalities that I'm required to solve in the current exercise it is clearly stated 'Find the positive values of X which satisfy both the inequalities.'

Now the format of the book is such that before making you solve any specific kind of problem yourself you are always given a 'worked example.'

Now my problem is that in the 'worked example' for this kind of problem 0 is not included as a positive value. The answer is given 0<X<3. Unfortunately when I go on to solve the first of these problems in the following exercise, in the 'answers' section of the book 0 is included as a positive value. I am certain that I've solved the two simultaneous inequalities correctly and they are (solved) X<8 and X<5. Following the methodology of the 'worked example' therefore, I've given my answer as 0<X<5. Unfortunately when I flip to the 'answers' section of my book, the correct answer provided suggests that I should have included 0 as a positive value: 0<X<5.

Is is the book trying to tell me that both ways are correct and that 0 can be either considered as positive or not included at all? Or does the book contain an error here? In short, is 0 to be considered as a positive value or not in the solution of this kind of inequality problem?

My Google searches have done little to clarify the situation. They tell me that in the English speaking world 0 is considered as neither positive nor negative, but that in the minds of the French 0 can be either positive or negative.

Any clarification on this matter would be much appreciated.

Many thanks,
Tom.
I fully agree with Otis that if the problem says to find positive answers and if your solution is correct, then the book's answer is in error. One reason, however, that we ask for the exact and complete wording of the question is that a student's paraphrase may miss some nuance that the original problem intended to convey. For example, if the problem asked for non-negative answers, then zero would be a valid answer. The definition of non-negative number is a positive number or zero. The standard definitions are:

$$\displaystyle x \text { is positive } \iff x > 0;$$

$$\displaystyle x \text { is negative } \iff x < 0;$$

$$\displaystyle x \text { is non-negative } \iff x \ge 0; \text { and }$$

$$\displaystyle x \text { is non-positive } \iff x \le 0.$$

#### Denis

##### Senior Member
If you make 0 errors, then that's a "positive" result

#### Otis

##### Senior Member
So when you make -1 errors, that's also a positive, no? Yes?

#### Denis

##### Senior Member
So when you make -1 errors, that's also a positive, no? Yes?

#### Jomo

##### Elite Member
If you make 0 errors, then that's a "positive" result
There must be a single word that describes you but I have not figured it out yet.

#### Jomo

##### Elite Member
Hi there,

As those of you who kindly answered my previous posts will know, I'm self studying algebra from a book called 'Teach yourself algebra: a complete introduction.' Now, all of my previous posts have been concerning specific problems, this one however, is a bit more general. I've reached the section on 'linear inequalities' and am having few difficulties in understanding the material, on one little detail however, my book is being somewhat ambiguous.

For the simultaneous inequalities that I'm required to solve in the current exercise it is clearly stated 'Find the positive values of X which satisfy both the inequalities.'

Now the format of the book is such that before making you solve any specific kind of problem yourself you are always given a 'worked example.'

Now my problem is that in the 'worked example' for this kind of problem 0 is not included as a positive value. The answer is given 0<X<3. Unfortunately when I go on to solve the first of these problems in the following exercise, in the 'answers' section of the book 0 is included as a positive value. I am certain that I've solved the two simultaneous inequalities correctly and they are (solved) X<8 and X<5. Following the methodology of the 'worked example' therefore, I've given my answer as 0<X<5. Unfortunately when I flip to the 'answers' section of my book, the correct answer provided suggests that I should have included 0 as a positive value: 0<X<5.

Is is the book trying to tell me that both ways are correct and that 0 can be either considered as positive or not included at all? Or does the book contain an error here? In short, is 0 to be considered as a positive value or not in the solution of this kind of inequality problem?

My Google searches have done little to clarify the situation. They tell me that in the English speaking world 0 is considered as neither positive nor negative, but that in the minds of the French 0 can be either positive or negative.

Any clarification on this matter would be much appreciated.

Many thanks,
Tom.
Tom, before I say that the book is correct or not I would like to see the problem.

If the answer to your problems are X<8 and X<5, then all negative numbers are included in both solutions as for example -3<8 and -4<5

##### New member
Thanks

Hi there,

Thanks for your help. If anyone would like to see the problem it's as follows:

Find the positive values of X which satisfy both the inequalities:

2x<x+8 and 5+2x>3x

Best regards,
Tom

#### Denis

##### Senior Member
Find the positive values of x which satisfy both the inequalities:

2x < x+8 and 5+2x > 3x
Helps by having "a look" at "what if they're equal?":

2x = x + 8 : x = 8

3x = 2x + 5 : x = 5

#### Jomo

##### Elite Member
Hi there,

Thanks for your help. If anyone would like to see the problem it's as follows:

Find the positive values of X which satisfy both the inequalities:

2x<x+8 and 5+2x>3x

Best regards,
Tom
x<8 AND x< 5 AND x>0. Combing these we get 0< x <5. So you are correct when you say that the answer in the back of the book is wrong

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#### klimbo

##### New member
Hi there,

As those of you who kindly answered my previous posts will know, I'm self studying algebra from a book called 'Teach yourself algebra: a complete introduction.' Now, all of my previous posts have been concerning specific problems, this one however, is a bit more general. I've reached the section on 'linear inequalities' and am having few difficulties in understanding the material, on one little detail however, my book is being somewhat ambiguous.

For the simultaneous inequalities that I'm required to solve in the current exercise it is clearly stated 'Find the positive values of X which satisfy both the inequalities.'

Now the format of the book is such that before making you solve any specific kind of problem yourself you are always given a 'worked example.'

Now my problem is that in the 'worked example' for this kind of problem 0 is not included as a positive value. The answer is given 0<X<3. Unfortunately when I go on to solve the first of these problems in the following exercise, in the 'answers' section of the book 0 is included as a positive value. I am certain that I've solved the two simultaneous inequalities correctly and they are (solved) X<8 and X<5. Following the methodology of the 'worked example' therefore, I've given my answer as 0<X<5. Unfortunately when I flip to the 'answers' section of my book, the correct answer provided suggests that I should have included 0 as a positive value: 0<X<5.

Is is the book trying to tell me that both ways are correct and that 0 can be either considered as positive or not included at all? Or does the book contain an error here? In short, is 0 to be considered as a positive value or not in the solution of this kind of inequality problem?

My Google searches have done little to clarify the situation. They tell me that in the English speaking world 0 is considered as neither positive nor negative, but that in the minds of the French 0 can be either positive or negative
.

Any clarification on this matter would be much appreciated.

Many thanks,

Tom.
hi
i think If you make 0 errors i think you will find a positive result but you must make 0 errors

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#### HallsofIvy

##### Elite Member
Hi there,

Thanks for your help. If anyone would like to see the problem it's as follows:

Find the positive values of X which satisfy both the inequalities:

2x<x+8 and 5+2x>3x

Best regards,
Tom
First, if I were really hard nosed I would say there is NO value of "X" that satisfies those equations, because those equations use "x", not "X"!

Assuming you mean "Find the values of x that satisfy both the inqualities:
2x< x+ 8 and 5+ 2x> 3x" (notice that I have emphasized the word "both"- I think you were treating these as two separate problems- and dropped the word "positive").
If x satisfies 2x< x+ 8 then 2x- x= x< 8 and if x satisfies 5+ 2x> 3x then 5> 3x- 2x= x. If x satisfies both then 5<x and x< 8 or 5< x< 8. The word "positive" was not necessary in the problem statement because only positive numbers satisfy the two inequalities. And there is no question about "0" because 0 is already less than 5.