## Easy Algebra Step-by-Step: Master High-Frequency Concepts and Skills for Algebra Proficiency—FAST! (2012)

### Answer Key

**Chapter 1 Numbers of Algebra****Exercise 1**

__1__. 10 is a natural number, a whole number, an integer, a rational number, and a real number.

__2__. is a rational number and a real number.

__3__. is a rational number and a real number.

__4__. –*π* is an irrational number and a real number.

__5__. –1000 is an integer, a rational number, and a real number.

__6__. is an irrational number and a real number.

__7__. is an irrational number and a real number.

__8__. is a rational number and a real number.

__9__. 1 is a natural number, a whole number, an integer, a rational number, and a real number.

__10__. = 0.1 is a rational number and a real number.

__11__. Closure property of multiplication

__12__. Commutative property of addition

__13__. Multiplicative inverse property

__14__. Closure property of addition

__15__. Associative property of addition

__16__. Distributive property

__17__. Additive inverse property

__18__. Zero factor property

__19__. Associative property of multiplication

__20__. Multiplicative identity property

**Chapter 2 Computation with Real Numbers****Exercise 2**

__3__.

__4__. “Negative nine plus the opposite of negative four equals negative nine plus four”

__5__. “Negative nine minus negative four equals negative nine plus four”

__8__.

__9__.

__11__.

__12__.

__14__.

__15__.

__17__.

__18__.

__19__.

**Chapter 3 Roots and Radicals****Exercise 3**

__2__.

__5__.

__7__.

__8__.

__9__.

__10__.

__11__.

__12__.

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__15__.

__16__.

__18__.

__19__.

__20__.

**Chapter 4 Exponentiation****Exercise 4**

__5__.

__9__.

__10__.

__11__.

__12__.

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__16__.

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__20__.

**Chapter 5 Order of Operations****Exercise 5**

__5__.

**Chapter 6 Algebraic Expressions****Exercise 6**

__1__. Name the variable(s) and constant(s) in the expression 2π *r*, where *r* is the measure of the radius of a circle. Answer: The letter *r* stands for the measure of the radius of a circle and can be any real nonzero number, so *r* is a variable. The numbers 2 and *π* have fixed, definite values, so they are constants.

__2__. –12 is the numerical coefficient

__3__. 1 is the numerical coefficient

__4__. is the numerical coefficient

__11__.

__13__.

__14__.

__16__.

**Chapter 7 Rules for Exponents****Exercise 7**

__3__.

__4__.

__5__.

__10__.

__11__.

__12__. (2*x* + 1)^{2} is a power of a sum. It cannot be simplified using only rules for exponents.

__13__. (3*x* – 5)^{3} is a power of a difference. It cannot be simplified using only rules for exponents.

__15__.

**Chapter 8 Adding and Subtracting Polynomials****Exercise 8**

**Chapter 9 Multiplying Polynomials****Exercise 9**

**Chapter 10 Simplifying Polynomial Expressions****Exercise 10**

**Chapter 11 Dividing Polynomials****Exercise 11**

The quotient is and the remainder is 0.

The quotient is and the remainder is 0.

__3__.

The quotient is and the remainder is 0.

The quotient is and the remainder is 0.

The quotient is and the remainder is 0.

__6__.

The quotient is –6 and the remainder is 5.

The quotient is and the remainder is 0.

__8__.

The quotient is *x* – 1 and the remainder is 0.

__9__.

The quotient is *x*–5 and the remainder is 0.

__10__.

The quotient is and the remainder is 98.

**Chapter 12 Factoring Polynomials****Exercise 12**

__1__. False

__2__. False

__3__. False

__4__. False

__5__. False

**Chapter 13 Rational Expressions****Exercise 13**

__1__.

__2__.

__3__.

__4__. is simplified.

__5__.

__6__.

__8__.

__9__.

__10__.

__11__.

__12__.

__13__.

__14__.

__15__.

**Chapter 14 Solving Linear Equations and Inequalities****Exercise 14**

__2__.

__4__.

**Chapter 15 Solving Quadratic Equations****Exercise 15**

There is no real solution because the discriminant is negative.

**Chapter 16 The Cartesian Coordinate Plane****Exercise 16**

__1__. True

__2__. False

__3__. True

__4__. False

__5__. True

__6__. False

__7__. rise

__8__. run

__9__. negative

__10__. positive

__11__. zero

__12__.

__13__.

__14__. undefined

__15__.

The point *K* is 6 units to the left of the *y*-axis and 5 units below the *x*-axis, so (–6, –5) is the ordered pair corresponding to point *K*.

__16__.

__17__.

__18__.

__19__.

__20__.

**Chapter 17 Graphing Linear Equations**

**Exercise 17**

__1__.

__6__.

**Chapter 18 The Equation of a Line**

**Exercise 18**

__3__.

__7__.

__10__.

**Chapter 19 Basic Function Concepts****Exercise 19**

Only *f*, *h*, and *t* are functions. Note that in *t*, (8, 9) and (8, 9) are the same point.

__2__. The domain is {4, 6, 7, 8} and the range is {5, 7, 9}.

The domain is the set of all real numbers.

b.

· The domain is the set of all real numbers greater than or equal to

c. The domain is the set of all real numbers except 5.

d.

Set and solve.

*x* = ±2 The domain is the set of all real numbers except 2 and –2.

__4__. a.

b.

c.

d. There is no real number solution because the square root of a negative number is not a real number.

__5__. Only graphs b and c are functions.

**Chapter 20 Systems of Equations****Exercise 20**