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# College Algebra 11th

## Educators

### Problem 1

The fact that $2(x+3)=2 x+6$ is attributable to the ___________ Property.

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### Problem 2

The fact that $3 x=0$ implies that $x=0$ is a result of the _____________ Property.

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### Problem 3

The domain of the variable in the expression $\frac{x}{x-4}$ is __________.

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### Problem 4

True or False
Multiplying both sides of an equation by any number results in an equivalent equation.

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### Problem 5

An equation that is satisfied for every value of the variable for which both sides are defined is called a(n) ________.

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### Problem 6

An equation of the form $a x+b=0$ is called a(n) _______ equation or a(n) ___________ equation

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### Problem 7

True or False
The solution of the equation $3 x-8=0$ is $\frac{3}{8}$

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### Problem 8

True or False
Some equations have no solution.

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### Problem 9

Multiple Choice
An admissible value for the variable that makes the equation a true statement is called a(n) ______ of the equation.
(a) identity
(b) solution
(c) degree
(d) model

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### Problem 10

Multiple Choice
A chemist mixes 10 liters of a $20 \%$ solution with $x$ liters of a $35 \%$ solution. Which of the following expressions represents the total number of liters in the mixture?
(a) $x$
(b) $20-x$
(c) $\frac{35}{x}$
(d) $10+x$

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### Problem 11

Mentally solve each equation.
$7 x=21$

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### Problem 12

Mentally solve each equation.
$6 x=-24$

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### Problem 13

Mentally solve each equation.
$$3 x+15=0$$

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### Problem 14

Mentally solve each equation.
$$6 x+18=0$$

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### Problem 15

Mentally solve each equation.
$$2 x-3=0$$

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### Problem 16

Mentally solve each equation.
$$3 x+4=0$$

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### Problem 17

Mentally solve each equation.
$$\frac{1}{4} x=\frac{7}{20}$$

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### Problem 18

Mentally solve each equation.
$$\frac{2}{3} x=\frac{9}{2}$$

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### Problem 19

Solve each equation, if possible.
$$3 x+4=x$$

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### Problem 20

Solve each equation, if possible.
$$2 x+9=5 x$$

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### Problem 21

Solve each equation, if possible.
$$2 t-6=3-t$$

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### Problem 22

Solve each equation, if possible.
$$5 y+6=-18-y$$

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### Problem 23

Solve each equation, if possible.
$6-x=2 x+9$

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### Problem 24

Solve each equation, if possible.
$3-2 x=2-x$

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### Problem 25

Solve each equation, if possible.
$$3+2 n=4 n+7$$

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### Problem 26

Solve each equation, if possible.
$$6-2 m=3 m+1$$

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### Problem 27

Solve each equation, if possible.
$$3(5+3 x)=8(x-1)$$

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### Problem 28

Solve each equation, if possible.
$$3(2-x)=2 x-1$$

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### Problem 29

Solve each equation, if possible.
$$8 x-(3 x+2)=3 x-10$$

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### Problem 30

Solve each equation, if possible.
$$7-(2 x-1)=10$$

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### Problem 31

Solve each equation, if possible.
$$\frac{3}{2} x+2=\frac{1}{2}-\frac{1}{2} x$$

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### Problem 32

Solve each equation, if possible.
$$\frac{1}{3} x=2-\frac{2}{3} x$$

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### Problem 33

Solve each equation, if possible.
$$\frac{1}{2} x-5=\frac{3}{4} x$$

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### Problem 34

Solve each equation, if possible.
$$1-\frac{1}{2} x=6$$

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### Problem 35

Solve each equation, if possible.
$$\frac{2}{3} p=\frac{1}{2} p+\frac{1}{3}$$

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### Problem 36

Solve each equation, if possible.
$$\frac{1}{2}-\frac{1}{3} p=\frac{4}{3}$$

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### Problem 37

Solve each equation, if possible.
$$0.2 m=0.9+0.5 m$$

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### Problem 38

Solve each equation, if possible.
$$0.9 t=1+t$$

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### Problem 39

Solve each equation, if possible.
$$\frac{x+1}{3}+\frac{x+2}{7}=2$$

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### Problem 40

Solve each equation, if possible.
$$\frac{2 x+1}{3}+16=3 x$$

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### Problem 41

Solve each equation, if possible.
$$\frac{5}{8}(p+3)-2=\frac{1}{4}(2 p-3)+\frac{11}{16}$$

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### Problem 42

Solve each equation, if possible.
$$\frac{1}{3}(w+1)-3=\frac{2}{5}(w-4)-\frac{2}{15}$$

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### Problem 43

Solve each equation, if possible.
$$\frac{2}{y}+\frac{4}{y}=3$$

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### Problem 44

Solve each equation, if possible.
$$\frac{4}{y}-5=\frac{5}{2 y}$$

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### Problem 45

Solve each equation, if possible.
$$\frac{1}{2}+\frac{2}{x}=\frac{3}{4}$$

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### Problem 46

Solve each equation, if possible.
$$\frac{3}{x}-\frac{1}{3}=\frac{1}{6}$$

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### Problem 47

Solve each equation, if possible.
$$(x+7)(x-1)=(x+1)^{2}$$

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### Problem 48

Solve each equation, if possible.
$$(x+2)(x-3)=(x+3)^{2}$$

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### Problem 49

Solve each equation, if possible.
$$x(2 x-3)=(2 x+1)(x-4)$$

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### Problem 50

Solve each equation, if possible.
$$x(1+2 x)=(2 x-1)(x-2)$$

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### Problem 51

Solve each equation, if possible.
$$p\left(p^{2}+3\right)=12+p^{3}$$

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### Problem 52

Solve each equation, if possible.
$$w\left(4-w^{2}\right)=8-w^{3}$$

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### Problem 53

Solve each equation, if possible.
$$\frac{x}{x-2}+3=\frac{2}{x-2}$$

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### Problem 54

Solve each equation, if possible.
$$\frac{2 x}{x+3}=\frac{-6}{x+3}-2$$

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### Problem 55

Solve each equation, if possible.
$$\frac{2 x}{x^{2}-4}=\frac{4}{x^{2}-4}-\frac{3}{x+2}$$

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### Problem 56

Solve each equation, if possible.
$$\frac{x}{x^{2}-9}+\frac{4}{x+3}=\frac{3}{x^{2}-9}$$

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### Problem 57

Solve each equation, if possible.
$$\frac{x}{x+2}=\frac{3}{2}$$

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### Problem 58

Solve each equation, if possible.
$$\frac{3 x}{x-1}=2$$

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### Problem 59

Solve each equation, if possible.
$$\frac{7}{3 x+10}=\frac{2}{x-3}$$

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### Problem 60

Solve each equation, if possible.
$$\frac{-4}{x+4}=\frac{-3}{x+6}$$

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### Problem 61

Solve each equation, if possible.
$$\frac{6 t+7}{4 t-1}=\frac{3 t+8}{2 t-4}$$

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### Problem 62

Solve each equation, if possible.
$$\frac{8 w+5}{10 w-7}=\frac{4 w-3}{5 w+7}$$

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### Problem 63

Solve each equation, if possible.
$$\frac{4}{x-2}=\frac{-3}{x+5}+\frac{7}{(x+5)(x-2)}$$

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### Problem 64

Solve each equation, if possible.
$$\frac{-4}{2 x+3}+\frac{1}{x-1}=\frac{1}{(2 x+3)(x-1)}$$

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### Problem 65

Solve each equation, if possible.
$$\frac{2}{y+3}+\frac{3}{y-4}=\frac{5}{y+6}$$

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### Problem 66

Solve each equation, if possible.
$$\frac{5}{5 z-11}+\frac{4}{2 z-3}=\frac{-3}{5-z}$$

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### Problem 67

Solve each equation, if possible.
$$\frac{x}{x^{2}-9}-\frac{x-4}{x^{2}+3 x}=\frac{10}{x^{2}-3 x}$$

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### Problem 68

Solve each equation, if possible.
$$\frac{x+1}{x^{2}+2 x}-\frac{x+4}{x^{2}+x}=\frac{-3}{x^{2}+3 x+2}$$

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### Problem 69

Use a calculator to solve each equation. Round the solution to two decimal places.
$$3.2 x+\frac{21.3}{65.871}=19.23$$

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### Problem 70

Use a calculator to solve each equation. Round the solution to two decimal places.
$$6.2 x-\frac{19.1}{83.72}=0.195$$

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### Problem 71

Use a calculator to solve each equation. Round the solution to two decimal places.
$$14.72-21.58 x=\frac{18}{2.11} x+2.4$$

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### Problem 72

Use a calculator to solve each equation. Round the solution to two decimal places.
$$18.63 x-\frac{21.2}{2.6}=\frac{14}{2.32} x-20$$

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### Problem 73

Solve each equation. The letters $a, b,$ and $c$ are constants.
$a x-b=c, \quad a \neq 0$

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### Problem 74

Solve each equation. The letters $a, b,$ and $c$ are constants.
$1-a x=b, \quad a \neq 0$

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### Problem 75

Solve each equation. The letters $a, b,$ and $c$ are constants.
$\frac{x}{a}+\frac{x}{b}=c, a \neq 0, b \neq 0, a \neq-b$

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### Problem 76

Solve each equation. The letters $a, b,$ and $c$ are constants.
$\frac{a}{x}+\frac{b}{x}=c, \quad c \neq 0$

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### Problem 77

Find the number $a$ for which $x=4$ is a solution of the equation.
$$x+2 a=16+a x-6 a$$

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### Problem 78

Find the number $b$ for which $x=2$ is a solution of the equation.
$$x+2 b=x-4+2 b x$$

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### Problem 79

List some formulas that occur in applications. Solve each formula for the indicated variable.
Electricity $\frac{1}{R}=\frac{1}{R_{1}}+\frac{1}{R_{2}}$ for $R$

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### Problem 80

List some formulas that occur in applications. Solve each formula for the indicated variable.
Finance $A=P(1+r t)$ for $r$

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### Problem 81

List some formulas that occur in applications. Solve each formula for the indicated variable.
Mechanics $F=\frac{m v^{2}}{R}$ for $R$

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### Problem 82

List some formulas that occur in applications. Solve each formula for the indicated variable.
Chemistry $P V=n R T$ for $T$

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### Problem 83

List some formulas that occur in applications. Solve each formula for the indicated variable.
Mathematics $S=\frac{a}{1-r}$ for $r$

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### Problem 84

List some formulas that occur in applications. Solve each formula for the indicated variable.
Mechanics $v=-g t+v_{0} \quad$ for $t$

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### Problem 85

A total of $\$ 20,000$is to be invested, some in bonds and some in certificates of deposit (CDs). If the amount invested in bonds is to exceed that in CDs by$\$3000$, how much will be invested in each type of investment?

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### Problem 86

A total of $\$ 10,000$is to be divided between Sean and George, with George to receive$\$3000$ less than Sean. How much will each receive?

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### Problem 89

Going into the final exam, which will count as two tests, Brooke has test scores of 80,83,71,61 , and $95 .$ What score does Brooke need on the final in order to have an average score of $80 ?$

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### Problem 90

Going into the final exam, which will count as two-thirds of the final grade, Mike has test scores of $86,80,84,$ and $90 .$ What minimum score does Mike need on the final in order to earn a B, which requires an average score of $80 ?$ What does he need to earn an $A$, which requires an average of $90 ?$

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### Problem 102

Find the largest perimeter of an isosceles triangle whose sides are of lengths $4 x+10,2 x+40$, and $3 x+18$.

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### Problem 103

Solve:
$\frac{3}{4} x-\frac{1}{5}\left(\frac{1}{2}-3 x\right)+1=\frac{1}{4}\left(\frac{1}{20} x+6\right)-\frac{4}{5}$

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### Problem 104

A regular hexagon is inscribed in a circle. Find the radius of the circle if the perimeter of the hexagon is 10 inches more than the radius.

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### Problem 105

One step in the following list contains an error. Identify it and explain what is wrong.
\begin{aligned}x &=2 \quad (1) \\3 x-2 x &=2 \quad (2) \\3 x &=2 x+2 \quad (3) \\x^{2}+3 x &=x^{2}+2 x+2\quad (4) \\x^{2}+3 x-10 &=x^{2}+2 x-8\quad (5) \\(x-2)(x+5) &(x2(x+4)\quad(6)\\x+5 &=x+4\quad(7) \\1 &=0\quad(8)\end{aligned}

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### Problem 106

The equation
$$\frac{5}{x+3}+3=\frac{8+x}{x+3}$$
has no solution, yet when we go through the process of solving it, we obtain $x=-3 .$ Write a brief paragraph to explain what causes this to happen.

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### Problem 107

Make up an equation that has no solution and give it to a fellow student to solve. Ask the fellow student to write a critique of your equation.

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