# the sign of expression − a .

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.1, Problem 80E

(a)

To determine

## To identify: the sign of expression −a .

Expert Solution

a<0

### Explanation of Solution

Given information:

Three real numbers a,b,c such that a>0,b<0 , and c<0 .

Calculation:

Consider the given expression.

a

Now, a>0

So, sign of a can be determined as shown:

(+)=()

So, a<0 .

(b)

To determine

Expert Solution

b>0

### Explanation of Solution

Given information:

Three real numbers a,b,c such that a>0,b<0 , and c<0 .

Calculation:

Consider the given expression.

b

Now, b<0

So, sign of b can be determined as shown:

()=(+)

So, b>0 .

(c)

To determine

Expert Solution

bc>0

### Explanation of Solution

Given information:

Three real numbers a,b,c such that, a>0,b<0 and c<0 .

Calculation:

Consider the given expression.

bc

Now, a>0,b<0 and c<0 .

So, sign of bc can be determined as shown:

()()=(+)

So, bc>0 .

(d)

To determine

Expert Solution

ab>0

### Explanation of Solution

Given information:

Three real numbers a,b,c such that, a>0,b<0 and c<0 .

Calculation:

Now, a>0,b<0 and c<0 .

So, sign of ab can be determined as shown:

((+)())=((+)(+))=(+)

So, ab>0 .

(e)

To determine

Expert Solution

ca<0

### Explanation of Solution

Given information:

Three real numbers a,b,c such that, a>0,b<0 and c<0 .

Calculation:

Consider the given expression.

ca

Now, a>0,b<0 and c<0 .

So, sign of ca can be determined as shown:

(())=()(+)=()

So, ca<0 .

(f)

To determine

Expert Solution

a+bc>0

### Explanation of Solution

Given information:

Three real numbers a,b,c such that, a>0,b<0 and c<0 .

Calculation:

Consider the given expression.

a+bc

Now, a>0,b<0 and c<0 .

So, sign of a+bc can be determined as shown:

(+)+()()=(+)+(+)=(+)

So, a+bc>0 .

(g)

To determine

Expert Solution

ab+ac<0

### Explanation of Solution

Given information:

Three real numbers a,b,c such that, a>0,b<0 and c<0 .

Calculation:

Consider the given expression.

ab+ac

Now, a>0,b<0 and c<0 .

So, sign of ab+ac can be determined as shown:

(+)()+(+)()=()+()=()

So, ab+ac<0 .

(h)

To determine

Expert Solution

abc<0

### Explanation of Solution

Given information:

Three real numbers a,b,c such that, a>0,b<0 and c<0 .

Calculation:

Consider the given expression.

abc

Now, a>0,b<0 and c<0 .

So, sign of abc can be determined as shown:

(+)()()=()(+)(+)=()

So, abc<0 .

(i)

To determine

Expert Solution

ab2>0

### Explanation of Solution

Given information:

Three real numbers a,b,c such that, a>0,b<0 and c<0 .

Calculation:

Consider the given expression.

ab2

Now, a>0,b<0 and c<0 .

So, sign of ab2 can be determined as shown:

(+)()2=(+)(+)=(+)

So, ab2>0 .

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