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Solve the equation.

4x - 3 = 2x + 3

Solve the equation.

5 - (6x + 3) = 2(2 - 2x)

Solve the equation.

x(x + 6) = 9

Solve the equation.

x2 = 8x - 12

Solve the equation.

√x + 2 + 5 = √x + 15

Solve the equation.

5/x + 3 - 6/x - 2 = 3/x2 + x - 6

Solve the equation.

3x + 4/3 - 2x/x - 3 = x

Solve the equation.

x/2 + 4/3 x = x + 5

Solve the equation.

5 - 2/x + 1/x2 = 0

Solve the equation.

(2x + 1)2 = 9

Solve the equation.

x -2/5 - 2x -1/5 - 15 = 0

Solve the equation.

√x + 2 + 1 = √2x + 6

Solve the equation.

x4 - 3x2 - 4 = 0

Solve the equation.

1.2x + 0.3 = 0.7x - 0.9

This section of miscellaneous equations provides practice in solving all the types introduced in this chapter so far. Solve each equation.

3√2x + 1 = 3√9

Solve the equation.

3x2 - 2x = -1

Solve the equation.

3[2x - (6 - 2x) + 1] = 5x

Solve the equation.

√x + 1 = √11 - √x

Solve the equation.

(14 - 2x)2/3 = 4

Solve the equation.

-x-2 + 2x-1 = 1

Solve the equation.

3/x - 3 = 3/x - 3

Solve the equation.

a2 + b2 = c2, for a

Match the inequality in each exercise in Column I with its equivalent interval notation in Column II.

x < -6

A. (-2, 6]

B. [-2, 6)

C. (-∞, -6)

D. [6, ∞)

E. (-∞, -3) ⋃ (3, ∞)

F. (-∞, -6)

G. (0, 8)

H. (-∞, ∞)

I. (-6, ∞)

J. (-∞, 6)

For the rectangular parking area of the shopping center shown, with x in yards, which one of the following equations says that the area is 40,000 yd2?


A. x(2x + 200) = 40,000 

B. 2x + 2(2x + 200) = 40,000

C. x + (2x + 200) = 40,000 

D. x2 + (2x + 200)2 = 40,0002

Fill in the blank to correctly complete each sentence.

A(n)________ is an equation that has a rational expression for one or more terms.

Match each equation or inequality in Column I with the graph of its solution set in Column II.

|x| = 7

Fill in the blank to correctly complete each sentence.

By definition, i = ______, and therefore, i2 = ___________.

Match the inequality in each exercise in Column I with its equivalent interval notation in Column II.

x ≤ 6

A. (-2, 6]

B. [-2, 6)

C. (-∞, -6)

D. [6, ∞)

E. (-∞, -3) ⋃ (3, ∞)

F. (-∞, -6)

G. (0, 8)

H. (-∞, ∞)

I. (-6, ∞)

J. (-∞, 6)

If a rectangle is r feet long and s feet wide, which expression represents the length of its diagonal in terms of r and s?


A. √rs 

B. r + s 

C. √r2 + s2 

D. r2 + s2

Fill in the blank to correctly complete each sentence.

If a and b are real numbers, then any number of the form a + bi is a(n) ____________.

Match each equation or inequality in Column I with the graph of its solution set in Column II.

|x| = -7

Fill in the blank to correctly complete each sentence.

The numbers 6 + 5i and 6 - 5i, which differ only in the sign of their imaginary parts, are _________.

Solve each problem.

Time Traveled How long will it take a car to travel 400 mi at an average rate of 50 mph?

Fill in the blank to correctly complete each sentence.

A(n)____________ is a statement that two expressions are equal.

Solve each equation.

3(x - 4) - 5(x + 2) = 2 - (x + 24)

Match the equation in Column I with its solution(s) in Column II.

x2 = 25

Solve each equation.

2x + 8 = 3x + 2

Solve the linear equation 3(x - 5) + 2 = 1 - (4 + 2x).

Determine whether each equation is an identity, a conditional equation, or a contradiction. Give the solution set.

(a) 4x - 5 = -2(3 - 2x) + 3

(b) 5x - 9 = 5(-2 + x) + 1

(c) 5x - 4 = 3(6 - x)

Fill in the blank to correctly complete each sentence.

Proposed solutions for which any denominator equals____________are excluded from the solution set of a rational equation.

Solve each problem.

Distance Traveled If a train travels at 80 mph for 15 min, what is the distance traveled?

Solve each problem.

Investing If a person invests $500 at 2% simple interest for 4 yr, how much interest is earned?

Solve each equation.

Fill in the blank to correctly complete each sentence.

To__________ an equation means to find all numbers that make the equation a true statement.

Match the equation in Column I with its solution(s) in Column II.

x2 = –25

Solve each equation.

1/6 x - 1/2(x - 1) = 1/2

Solve the equation ay + 2x = y + 5x for y. (Assume a ≠ 1.)

Fill in the blank to correctly complete each sentence.

If a job can be completed in 4 hr, then the rate of work is_______of the job per hour.

To solve for the lengths of the right triangle sides, which equation is correct?


A. x2 = (2x - 2)2 + (x + 4)2

B. x2 + (x + 4)2 = (2x - 2)2

C. x2 = (2x - 2)2 - (x + 4)2

D. x2 + (2x - 2)2 = (x + 4)2


Match each equation or inequality in Column I with the graph of its solution set in Column II.

|x| > -7

Solve each equation.

6x2 - 11x - 7 = 0

Fill in the blank to correctly complete each sentence.

A__________ linear equation is a(n) because the greatest degree of the variable is 1.

Match the equation in Column I with its solution(s) in Column II.

x2 + 5 = 0

Solve each equation.

5x - 2(x + 4) = 3(2x + 1)

Solve each equation.

9x - 11(k + p) = x(a - 1)

Johnny deposits some money at 2.5% annual interest and twice as much at 3.0%. Find the amount deposited at each rate if his total annual interest income is $850.

Match the inequality in each exercise in Column I with its equivalent interval notation in Column II.

x2 ≥ 0

A. (-2, 6]

B. [-2, 6)

C. (-∞, -6)

D. [6, ∞)

E. (-∞, -3) ⋃ (3, ∞)

F. (-∞, -6)

G. (0, 8)

H. (-∞, ∞)

I. (-6, ∞)

J. (-∞, 6)

Fill in the blank to correctly complete each sentence.

When the power property is used to solve an equation, it is essential to check all proposed solutions in the_________.

The mat and frame around the picture shown measure x inches across. Which equation says that the area of the picture itself is 600 in.2?


A. 2(34 - 2x) + 2(21 - 2x) = 600

B. (34 - 2x)(21 - 2x) = 600

C. (34 - x)(21 - x) = 600

D. x(34)(21) = 600

Match each equation or inequality in Column I with the graph of its solution set in Column II.

|x| > 7

Fill in the blank to correctly complete each sentence.

The product of a complex number and its conjugate is always a(n) __________.

Solve each problem.

Value of Coins If a jar of coins contains 40 half-dollars and 200 quarters, what is the monetary value of the coins?

Solve each equation.

(3x + 12) = 8

Fill in the blank to correctly complete each sentence.

A(n)__________ is an equation satisfied by every number that is a meaningful replacement for the variable.

Match the equation in Column I with its solution(s) in Column II.

x2 – 5 = 0

Solve each equation.


(approximate annual interest rate)

One model for the minimum hourly wage in the United States for the period 1979–2014 is

y = 0.128x - 250.43,

where x represents the year and y represents the wage, in dollars. (Source: Bureau of Labor Statistics.) The actual 2008 minimum wage was $6.55. What does this model predict as the wage? What is the difference between the actual wage and the predicted wage?

Match the inequality in each exercise in Column I with its equivalent interval notation in Column II.

x ≥ -6

A. (-2, 6]

B. [-2, 6)

C. (-∞, -6)

D. [6, ∞)

E. (-∞, -3) ⋃ (3, ∞)

F. (-∞, -6)

G. (0, 8)

H. (-∞, ∞)

I. (-6, ∞)

J. (-∞, 6)

Fill in the blank to correctly complete each sentence.

An equation such as x3/2 = 8 is an equation with a(n)_________, because it contains a variable raised to an exponent that is a rational number.

A rectangular piece of metal is 5 in. longer than it is wide. Squares with sides 2 in. long are cut from the four corners, and the flaps are folded upward to form an open box. Which equation indicates that the volume of the box is 64 in.3?


A. (x + 1)(x - 4)(2) = 64 

B. x(x + 5)(2) = 64

C. (x + 1)(x - 4) = 64 

D. x(x + 5) = 64

Match each equation or inequality in Column I with the graph of its solution set in Column II.

|x| < 7

Fill in the blank to correctly complete each sentence.

To find the quotient of two complex numbers in standard form, multiply both the numerator and the denominator by the complex conjugate of the ________.

Solve each problem.

Acid Mixture If 120 L of an acid solution is 75% acid, how much pure acid is there in the mixture?

Solve each equation.

3x2 + 2x = -2

Match the equation in Column I with its solution(s) in Column II.

x2 = –20

Fill in the blank to correctly complete each sentence.

A(n)_________ is an equation that has no solution.

Write -4 + √-24/8 in standard form a + bi.

Solve each problem.

Which of the following cannot be a correct equation to solve a geometry problem, if x represents the measure of a side of a rectangle?

A. 2x + 2(x + 2) = 20

B. 2x + (15 + x) = -2

C. 8(x + 2) + 4x = 16 

D. 2x + 2(x - 3) = 10

Match the inequality in each exercise in Column I with its equivalent interval notation in Column II.

6 ≤ x

A. (-2, 6]

B. [-2, 6)

C. (-∞, -6)

D. [6, ∞)

E. (-∞, -3) ⋃ (3, ∞)

F. (-∞, -6)

G. (0, 8)

H. (-∞, ∞)

I. (-6, ∞)

J. (-∞, 6)

Match each equation or inequality in Column I with the graph of its solution set in Column II.

|x| ≥ 7

Match each equation in Column I with the correct first step for solving it in Column II.


A. Cube each side of the equation.

B. Multiply each side of the equation by x(x + 5).

C. Raise each side of the equation to the power 2/5.

D. Square each side of the equation.

E. Let u = (x + 5)1/3 and u2 = (x + )22/3.

Decide whether each statement is true or false. If false, correct the right side of the equation.

√–25 = 5i

Solve each problem.

Sale Price Suppose that a computer that originally sold for x dollars has been discounted 60%. Which one of the following expressions does not represent its sale price?

A. x - 0.60x

B. 0.40x

C. 4/10x

D. x - 0.60


If a projectile is launched vertically upward from the ground with an initial velocity of 60 ft per sec, neglecting air resistance, its height s (in feet) above the ground t seconds after projection is given by

s = -16t2 + 60t.

Which equation should be used to determine the time at which the height of the projectile reaches 40 ft?

A. s = -16(40)2 + 60 

B. s = -16(40)2 + 60(40)

C. 40 = -16t2 + 60t 

D. 40 = -16t2

Decide whether each statement is true or false.

The solution set of 2x + 5 = x - 3 is {-8}.

Solve each equation.

Match the equation in Column I with its solution(s) in Column II.

x2 = 20

Write the quotient 7 - 2i/2 + 4i in standard form a + bi.

If x represents the number of pennies in a jar in an applied problem, which of the following equations cannot be a correct equation for finding x?

A. 5x + 3 = 11 

B. 12x + 6 = -4

C. 100x = 50(x + 3) 

D. 6(x + 4) = x + 24

Match the inequality in each exercise in Column I with its equivalent interval notation in Column II.


A. (-2, 6]

B. [-2, 6)

C. (-∞, -6)

D. [6, ∞)

E. (-∞, -3) ⋃ (3, ∞)

F. (-∞, -6)

G. (0, 8)

H. (-∞, ∞)

I. (-6, ∞)

J. (-∞, 6)

Match each equation in Column I with the correct first step for solving it in Column II.

√x + 5 = 7

A. Cube each side of the equation.

B. Multiply each side of the equation by x(x + 5).

C. Raise each side of the equation to the power 2/5.

D. Square each side of the equation.

E. Let u = (x + 5)1/3 and u2 = (x + )22/3.

Decide whether each statement is true or false. If false, correct the right side of the equation.

√–4 · √-9 = –6

Match each equation or inequality in Column I with the graph of its solution set in Column II.

|x| ≤ 7

Solve each problem.

Acid Mixture Suppose two acid solutions are mixed. One is 26% acid and the other is 34% acid. Which one of the following concentrations cannot possibly be the concentration of the mixture?

A. 24%

B. 30% 

C. 31% 

D. 33%

If a projectile is launched vertically upward from the ground with an initial velocity of 45 ft per sec, neglecting air resistance, its height s (in feet) above the ground t seconds after projection is given by

s = -16t2 + 45t.

Which equation should be used to determine the height of the projectile after 2 sec?

A. s = 2(-16t2 + 45t) 

B. s = -16(2)2 + 45(2)

C. 2 = -16t2 + 45t 

D. 2 = -16t2

Solve each equation.

Decide whether each statement is true or false.

The equation 5(x - 8) = 5 x - 40 is an example of an identity.

Match the equation in Column I with its solution(s) in Column II.

x – 5 = 0

Solve each equation.

3x2 - x = -1

Carry-on rules for domestic economy-class travel differ from one airline to another, as shown in the table.

Airline........................................ Size (linear inches)

Alaska..................................................... 51

American................................................ 45

Delta....................................................... 45

Southwest.............................................. 50

United......................................................45

USAirways.............................................. 45


To determine the number of linear inches for a carry-on, add the length, width, and height of the bag.

(a) One Samsonite rolling bag measures 9 in. by 12 in. by 21 in. Are there any airlines that would not allow it as a carry-on?

(b) A Lark wheeled bag measures 10 in. by 14 in. by 22 in. On which airlines does it qualify as a carry-on?

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