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College Algebra
Equations and Inequalities

1
Linear Equations and Applications

Problem  1
practice icon

Solve the following equation for \(x\).
\(3(x+2)-2=4x\)

Choose instructor to watch:
Saba cc
Saba
Lauren cc
Lauren
Gordon cc
Gordon
Julieta cc espanol spanish
Julieta
Problem  2
practice icon

Solve the equation:

\(\dfrac{x+5}{2}+\dfrac{2x-1}{5}=5\)

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Mr. Hampton cc
Mr. Hampton
Lauren cc
Lauren
Breylor cc
Breylor
Octabio cc espanol spanish
Octabio
Problem  3
practice icon

Solve the equation:

\(0.3(x+2)-0.02x=0.5\)

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Lauren cc
Lauren
Breylor cc
Breylor
Julieta cc espanol spanish
Julieta
Problem  4
practice icon

The perimeter of a rectangular fence is \(15\) feet. Write the width of the fence in terms of the length.

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Mr. Hampton cc
Mr. Hampton
Lauren cc
Lauren
Breylor cc
Breylor
Julieta cc espanol spanish
Julieta
Problem  5

Jon took out a loan at \(4\%\) simple interest and repaid it after \(5\) years. The total amount paid back was \(\$5760\), equal to the principal and interest. What was the principal?

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Julieta cc
Julieta
Julieta cc espanol spanish
Julieta
Problem  6

A \(20\)-foot tall white oak tree grows at a rate of \(0.8\) feet per year. How long will it take for the tree to reach a height of \(32\) feet?

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Julieta cc
Julieta
Julieta cc espanol spanish
Julieta

2
Quadratic Equations and Applications

Problem  1
practice icon

Solve \(2x^2-7x+3=0\) by factoring.

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Lauren cc
Lauren
Gordon cc
Gordon
Octabio cc espanol spanish
Octabio
Problem  2
practice icon

Solve \(-3x^2+9=0\)

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Lauren cc
Lauren
Breylor cc
Breylor
Julieta cc espanol spanish
Julieta
Problem  3
practice icon

Solve the equation \(3x^2-6x-1=0\) by using the technique of completing the square.

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Lauren cc
Lauren
Gordon cc
Gordon
Julieta cc espanol spanish
Julieta
Problem  4
practice icon

Solve the equation \(-4x^2+3x+\dfrac{1}{2}=0\) by using the quadratic formula.

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Mr. Hampton cc
Mr. Hampton
Lauren cc
Lauren
Gordon cc
Gordon
Julieta cc espanol spanish
Julieta
Problem  5
practice icon

Use the quadratic formula to find the real solutions of the equation \(-2t^2+3t=5\). Find the value of the discriminant.

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Mr. Hampton cc
Mr. Hampton
Lauren cc
Lauren
Gordon cc
Gordon
Octabio cc espanol spanish
Octabio
Problem  6
practice icon

The height of a ball after being thrown vertically upward from a point \(80\) feet above the ground with a velocity of \(40\) feet per second is given by \(h=-16t^2+40t+80\), where \(t\) is the time in seconds since the ball was thrown and \(h\) is in feet.

  1. When will the ball be \(50\) feet above the ground?

  2. When will the ball reach the ground?

  3. For what values of \(t\) does this problem make sense (from a physical sense)?

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Mr. Hampton cc
Mr. Hampton
Lauren cc
Lauren
Gordon cc
Gordon
Julieta cc espanol spanish
Julieta
Problem  7

The mobility rate (the percentage of people who changed residence) for the years 2000-2016 can be modeled by the equation \(y=0.0072t^2+0.0766t+11.318\), where \(t\) is the number of years since 2000. In what year between 2000 and 2016 was the mobility rate \(12\) percent?

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Julieta cc
Julieta
Julieta cc espanol spanish
Julieta

3
Complex Numbers and Quadratic Equations

Problem  1
practice icon

Write the following as pure imaginary numbers.

  1. \(\sqrt{-36}\)

  2. \(\sqrt{-8}\)

  3. \(\sqrt{-\dfrac{1}{4}}\)

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Saba cc
Saba
Shelby cc
Shelby
Breylor cc
Breylor
Julieta cc espanol spanish
Julieta
Problem  2

Write the following numbers in the form \(a+bi\), and identify \(a\) and \(b\).

  1. \(\sqrt{2}\)

  2. \(\dfrac{1}{3}i\)

  3. \(1+\sqrt{3}\)

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Mr. Hampton cc
Mr. Hampton
Shelby cc
Shelby
Breylor cc
Breylor
Julieta cc espanol spanish
Julieta
Problem  3

What are the real and imaginary parts of the following complex numbers?

  1. \(-2+3i\)

  2. \(-i+4\)

  3. \(-\sqrt{3}\)

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Saba cc
Saba
Shelby cc
Shelby
Breylor cc
Breylor
Julieta cc espanol spanish
Julieta
Problem  4
practice icon

Perform the following operations.

  1. \((1+2i)+(3-5i)\)

  2. \(\left(\sqrt{2}+i\right)+\left(-\sqrt{2}-i\right)\)

  3. \(i+(-1)\)

  4. \((1+i)-(2-i)\)

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Saba cc
Saba
Shelby cc
Shelby
Breylor cc
Breylor
Julieta cc espanol spanish
Julieta
Problem  5
practice icon

Multiply

  1. \((1+3i)(2-4i)\)

  2. \(\sqrt{-4}\sqrt{-9}\)

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Shelby cc
Shelby
Breylor cc
Breylor
Octabio cc espanol spanish
Octabio
Problem  6

Find the complex conjugates of the following numbers.

  1. \(1+2i\)

  2. \(-3i\)

  3. \(2\)

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Saba cc
Saba
Shelby cc
Shelby
Breylor cc
Breylor
Julieta cc espanol spanish
Julieta
Problem  7

Multiply \(-3+2i\) by its conjugate. What type of number results from the operation?

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Saba cc
Saba
Shelby cc
Shelby
Breylor cc
Breylor
Julieta cc espanol spanish
Julieta
Problem  8
practice icon

Find \(\dfrac{2}{-3+2i}\)

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Shelby cc
Shelby
Breylor cc
Breylor
Julieta cc espanol spanish
Julieta
Problem  9

Use the definition of \(i\) to solve the equation \(x^2=-4\).

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Shelby cc
Shelby
Breylor cc
Breylor
Octabio cc espanol spanish
Octabio
Problem  10

Find all solutions of the equation \(2x^2+2x+1=0\).

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Julieta cc
Julieta
Julieta cc espanol spanish
Julieta
Problem  11
practice icon

Find all solutions to the quadratic equation \(2t^2-2t=-\dfrac{3}{2}\). Relate the solutions of this equation to the zeros of an appropriate quadratic function.

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Saba cc
Saba
Shelby cc
Shelby
Breylor cc
Breylor
Julieta cc espanol spanish
Julieta

4
Other Types of Equations

Problem  1
practice icon

Solve the equation \(3x^4+5x^2-2=0\) for real values of \(x\).

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Lauren cc
Lauren
Gordon cc
Gordon
Julieta cc espanol spanish
Julieta
Problem  2

Solve the equation \(t^6-t^3=2\) for real values of \(t\).

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Lauren cc
Lauren
Gordon cc
Gordon
Breylor cc
Breylor
Problem  3

Solve \(\dfrac{4}{3x}=\dfrac{2}{x}+\dfrac{2}{3}\) and check your solution.

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Julieta cc
Julieta
Julieta cc espanol spanish
Julieta
Problem  4

Solve \(\dfrac{1}{x}=\dfrac{2}{x-2}+3\)

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Lauren cc
Lauren
Gordon cc
Gordon
Julieta cc espanol spanish
Julieta
Problem  5

Solve \(\dfrac{1}{x-2}=\dfrac{6}{x+3}+\dfrac{12}{x^2+x-6}\)

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Julieta cc
Julieta
Julieta cc espanol spanish
Julieta
Problem  6
practice icon

Solve \(\sqrt{3x+1}+2=x-1\)

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Lauren cc
Lauren
Gordon cc
Gordon
Julieta cc espanol spanish
Julieta
Problem  7
practice icon

Solve \(\sqrt{3x+1}-\sqrt{x+4}=1\)

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Gordon cc
Gordon
Octabio cc espanol spanish
Octabio
Problem  8

A theatre club arranged for a chartered bus trip to a play at a cost of \(\$350\). To lower costs, \(10\) nonmembers were invited to join the trip. The bus fare per person then decreased by \(\$4\). How many theatre club members were going on the trip?

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Mr. Hampton cc
Mr. Hampton
Lauren cc
Lauren
Gordon cc
Gordon
Julieta cc espanol spanish
Julieta
Problem  9

Jennifer is standing on one side of a river that is \(3\) kilometers wide. Her bus is located on the opposite side of the river. Jennifer plans to cross the river by rowboat and then jog the rest of the way to reach the bus, which is \(10\) kilometers along the river from point \(B\) directly across the river from her current location (point \(A\)). If she can row \(5\) kilometers per hour and jog \(7\) kilometers per hour, at which point on the other side of the river should she dock her boat so that it will take her a total of exactly two hours to reach the bus? Assume that Jennifer’s path on each leg of the trip is a straight line, and that there is no river current or wind speed.

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Lauren cc
Lauren
Gordon cc
Gordon
Julieta cc espanol spanish
Julieta

5
Linear Inequalities

Problem  1
practice icon

Solve \(x-4>-2x+2\)

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Lauren cc
Lauren
Gordon cc
Gordon
Breylor cc
Breylor
Problem  2

Solve the following inequalities:

  1. \(2x+\dfrac{5}{2}>3x-6\)

  2. \(-4\leq 3x-2<7\)

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Lauren cc
Lauren
Gordon cc
Gordon
Julieta cc espanol spanish
Julieta
Problem  3
practice icon

Alicia has a total of \(\$1\text{,}000\) to spend on a new computer system. If the sales tax is \(8\%\), what is the retail price range of computers that she should consider?

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Lauren cc
Lauren
Gordon cc
Gordon
Octabio cc espanol spanish
Octabio
Problem  4

T-Mobile offers two prepaid plans for their mobile phone customers.

  • Plan A charges \(\$3.00\) per month plus \(10\) cents per text message, whether sent or received.

  • Plan B charges a flat rate of \(\$45\) per month for unlimited text messages.

  1. Express the monthly cost for Plan A in terms of the number of text messages.

  2. Express the monthly cost for plan B in terms of the number of text messages.

  3. How many text messages would you have to send or receive per month for Plan B to be cheaper than Plan A.

Choose instructor to watch:
Julieta cc
Julieta
Julieta cc espanol spanish
Julieta
Problem  5
practice icon

To operate a gourmet coffee booth in a shopping mall, it costs \(\$500\) (the fixed cost) plus \(\$6\) for each pound of coffee bought at wholesale price. The coffee is then sold to customers for \(\$10\) per pound.

  1. Find an expression for the operating cost of selling \(q\) pounds of coffee.

  2. Find an expression for the revenue earned by selling \(q\) pounds of coffee.

  3. Find the break-even point.

  4. How many pounds of coffee must be sold for the revenue to be greater than the total cost?

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Lauren cc
Lauren
Gordon cc
Gordon
Julieta cc espanol spanish
Julieta

6
Equations and Inequalities Involving Absolute Value

Problem  1

Solve the following equations:

  1. \(\lvert 2x-3\rvert =7\)

  2. \(\lvert x \rvert = -3\)

  3. \(-\lvert 3x+1\rvert -3=-8\)

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Lauren cc
Lauren
Gordon cc
Gordon
Julieta cc espanol spanish
Julieta
Problem  2

Solve the following inequalities and indicate the solution set on a number line.

  1. \(\lvert 2x-3\rvert >7\)

  2. \(\left\lvert -\dfrac{2}{3}x+4\right\rvert \leq 57\)

  3. \(-4+\lvert 3-x\rvert >5\)

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Lauren cc
Lauren
Gordon cc
Gordon
Julieta cc espanol spanish
Julieta
Problem  3

Graph the following on a number line and write each set using an absolute value inequality.

  1. The set of all \(x\) whose distance from \(4\) is less than \(5\)

  2. The set of all \(x\) whose distance from \(4\) is greater than \(5\)

Choose instructor to watch:
Mr. Hampton cc
Mr. Hampton
Lauren cc
Lauren
Breylor cc
Breylor
Octabio cc espanol spanish
Octabio
Problem  4

A thermometer measures temperature with an uncertainty of \(0.25^\circ\text{F}\). If a person’s body temperature is measured at \(98.3^\circ\text{F}\), use absolute value notation to write an inequality for the range of possible body temperatures.

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Mr. Hampton cc
Mr. Hampton
Lauren cc
Lauren
Gordon cc
Gordon
Julieta cc espanol spanish
Julieta