Algebra Know-It-ALL

312 Review Questions and Answers

Question 12-4

Suppose we see the following equation where a,b,c, and d are constants and x is the

variable:

3 abx= 7 x/(c+d)

To be sure this equation makes sense, we must restrict the values of the constants. How?

Answer 12-4

We must require that c≠−d. That is, we can’t let c and d be additive inverses. If c and d

happen to be additive inverses, then we will find ourselves dividing by 0 on the right side of

the equation.

Question 12-5

Which of the following equations are first-degree equations in one variable? Which are not?

Lettersa,b, and c represent constants. Letters x,y, and z represent variables.

x+ 3 a+ 2 b=c

(c+a)x=b

(x+y)a=b

y^2 +ay+b=c

x+y+z= 0

Answer 12-5

The first and second equations are first-degree equations in one variable. The third and fifth

equations aren’t, because they contain more than one variable. The fourth equation isn’t,

because it contains the square of the variable.

Question 12-6

When using letters to represent constants, or when reading texts in which letters are used to

represent constants, we have to be clear and careful with the context. Why?

Answer 12-6

Some letters are widely used to represent specific physical, chemical, or mathematical

constants. In physics, c represents the speed of light in a vacuum; N is often used to

represent a chemical constant called the Avogadro constant; e is commonly used to

represent the exponential constant. We don’t want to let c be a general constant if we’re

writing about relativity theory, or N stand for a general constant if the subject happens

to be chemistry, or e indicate a general constant if the discussion involves exponential

functions.