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Intermediate Algebra
Linear Equations and Inequalities in One Variable

1
Linear Equations

Problem  1
practice icon

Determine whether 4 is a solution of 3x1=11.

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Molly S. cc
Molly S.
Octabio
Octabio
Cynthia espanol spanish
Cynthia
Problem  2
practice icon

Determine whether 12 is a solution of 13x+2=14x+1

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Molly S. cc
Molly S.
Octabio
Octabio
Cynthia espanol spanish
Cynthia
Problem  3
practice icon

Find the solution set for 3a5=6a+1

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Mr. McKeague cc
Mr. McKeague
Brooke cc
Brooke
David cc
David
David espanol spanish
David
Problem  4
practice icon

Solve 23x+12=38

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Mr. McKeague cc
Mr. McKeague
Arielle cc
Arielle
Matt cc
Matt
Cynthia espanol spanish
Cynthia
Study Skill

Common Mistake This is a mistake in using notation incorrectly.

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Mr. McKeague cc
Mr. McKeague
Problem  6
practice icon

Solve 0.06x+0.05(10,000x)=560

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Mr. McKeague cc
Mr. McKeague
Betsy cc
Betsy
Aaron cc
Aaron
Julieta espanol spanish
Julieta
Problem  7
practice icon

Solve 83(4x2)+5x=35

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Mr. McKeague cc
Mr. McKeague
Arielle cc
Arielle
David cc
David
David espanol spanish
David
Problem  8
practice icon

Solve 2(3x4)=3+6x

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Mr. McKeague cc
Mr. McKeague
Betsy cc
Betsy
Aaron cc
Aaron
Julieta cc espanol spanish
Julieta
Problem  9
practice icon

Solve 15+3x=3(x5)

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Mr. McKeague cc
Mr. McKeague
Betsy cc
Betsy
Anthony cc
Anthony
Anthony espanol spanish
Anthony

2
Formulas

Problem  1
practice icon

Find y when x=4 in the formula 3x+2y=6.

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Molly M. cc
Molly M.
Betsy
Betsy
Aaron
Aaron
David espanol spanish
David
Problem  2
practice icon

A store selling art supplies find that they can sell x sketch pads each week at p dollars each, according to the formula x=900300p. What price should they charge if they want to sell 525 pads each week?

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Aaron
Aaron
Brooke cc
Brooke
Edwin espanol spanish
Edwin
Julieta espanol spanish
Julieta
Problem  3
practice icon

A boat is traveling upstream against a current. If the speed of the boat in still water is r and the speed of the current is c then the formula for the distance traveled by the boat is d=(rc)t where t is time. Find c if d=52 miles, r=16 miles, and t=4 hours.

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Betsy cc
Betsy
Aaron cc
Aaron
Cynthia espanol spanish
Cynthia
Problem  4
practice icon

Given the formula P=2w+2l, solve for w.

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Molly S. cc
Molly S.
Betsy cc
Betsy
Logan cc
Logan
Cynthia espanol spanish
Cynthia
Problem  5
practice icon

Solve for x; ax3=bx+5

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Betsy cc
Betsy
Edwin espanol spanish
Edwin
Problem  6
practice icon

Solve for y: ybx0=m

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Betsy
Betsy
Graham
Graham
Edwin espanol spanish
Edwin
Problem  7
practice icon

Solve for y: y4x5=3

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Molly S. cc
Molly S.
Betsy cc
Betsy
Logan cc
Logan
Cynthia espanol spanish
Cynthia
Problem  8
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Solve for h: S=2πrh+2πr2

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Betsy
Betsy
Graham
Graham
Edwin espanol spanish
Edwin
Problem  9
practice icon

The first Ferris wheel had a diameter of 250 feet. It had 36 carriages and each of which held 40 people. One trip around took 20 minutes. Find the average speed of a rider. (Use 3.14 as an approximation for π).

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Betsy
Betsy
Graham
Graham
Cynthia espanol spanish
Cynthia

3
Applications

Problem  1
practice icon

The length of a rectangle is 3 inches less than twice the width. The perimeter is 45 inches. Find the length and width.

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Brooke cc
Brooke
Aaron cc
Aaron
Edwin espanol spanish
Edwin
Problem  2
practice icon

In April, Pat bought a Ford Mustang with a 5.0-liter engine. The total price, which includes the price of the car plus sales tax, was $17,481.75. If the sales tax rate was 7.25%, what was the price of the car?

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Ana
Ana
Aaron
Aaron
Julieta espanol spanish
Julieta
Problem  3
practice icon

Two complementary angles are such that one is twice as large as the other. Find the two angles.

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Stephanie cc
Stephanie
Aaron
Aaron
Cynthia espanol spanish
Cynthia
Problem  4
practice icon

A person invests $10,000 in two accounts. One account earns a 5% annually, and the other earns 6%. If the total interest earned in a year is $560, how much is invested in each account?

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Katrina cc
Katrina
Aaron cc
Aaron
Octabio espanol spanish
Octabio
Problem  5
practice icon

The base angles in an isosceles triangle are twice as large as the third angle. Find the measure of each angle.

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Molly S. cc
Molly S.
Octabio
Octabio
Cynthia espanol spanish
Cynthia
Problem  6

A piece of string 12 inches long is to be formed into a rectangle. Build a table that gives the length of the rectangle if the width is 1,2,3,4, or 5 inches. Then find the area of each of the rectangles formed.

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Katrina cc
Katrina
Graham
Graham
Cynthia espanol spanish
Cynthia

4
Interval Notation and Linear Inequalities

Problem  1

Introduction Using the properties for inequalities correctly and avoiding common mistakes.

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Mr. McKeague cc
Mr. McKeague
Problem  2
practice icon

Solve and graph: 3x+3<2x1

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Molly S. cc
Molly S.
Betsy cc
Betsy
David cc
David
David espanol spanish
David
Problem  3
practice icon

Solve: 2y37

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Mr. McKeague cc
Mr. McKeague
Molly S. cc
Molly S.
Matt cc
Matt
Julieta cc espanol spanish
Julieta
Problem  4
practice icon

Solve 3(2x4)7x3x

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Molly S. cc
Molly S.
Aaron cc
Aaron
David espanol spanish
David
Problem  5
practice icon

Solve and graph 2(13x)+4<4x14

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Stefanie cc
Stefanie
Preston cc
Preston
Edwin espanol spanish
Edwin
Problem  6
practice icon

Solve 2x3y<6 for y.

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Katrina cc
Katrina
CJ cc
CJ
Edwin espanol spanish
Edwin
Problem  7
practice icon

A company that manufactures ink cartridges finds that they can sell x cartridges each week at p dollars, according to x=1,300100p. What price should they charge if they want to sell at least 300 cartridges?

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Mrs. Mooney cc
Mrs. Mooney
Stefanie cc
Stefanie
Aaron cc
Aaron
Cynthia espanol spanish
Cynthia
Problem  8
practice icon

The formula F=95C+32 gives the relationship between Celsius and Fahrenheit. If the temperature on a certain day is 86 Fahrenheit, what is the temperature in degrees Celsius?

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Mr. McKeague cc
Mr. McKeague
Aaron cc
Aaron
Cynthia espanol spanish
Cynthia

5
Sets and Compound Inequalities

Problem  1
practice icon

Give an example of an infinite set.

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Stefanie
Stefanie
Aaron
Aaron
Edwin espanol spanish
Edwin
Problem  2
practice icon

Give an example of a finite set.

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Stefanie
Stefanie
Aaron
Aaron
Edwin espanol spanish
Edwin
Problem  3
practice icon

Let A={1,3,5}, B={0,2,4}, and C={1,2,3,}. Find AB.

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Suhas
Suhas
Katrina cc
Katrina
Logan cc
Logan
Edwin espanol spanish
Edwin
Problem  4
practice icon

Let A={1,3,5}, B={0,2,4}, and C={1,2,3,}. Find AB.

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Mr. Perez
Mr. Perez
Katrina cc
Katrina
Logan cc
Logan
Julieta cc espanol spanish
Julieta
Problem  5
practice icon

Let A={1,3,5}, B={0,2,4}, and C={1,2,3,}. Find AC.

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Mr. Perez
Mr. Perez
Katrina cc
Katrina
Logan cc
Logan
Edwin espanol spanish
Edwin
Problem  6
practice icon

Let A={1,3,5}, B={0,2,4}, and C={1,2,3,}. Find BC.

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Mr. Perez
Mr. Perez
Katrina cc
Katrina
Logan cc
Logan
Julieta cc espanol spanish
Julieta
Problem  7
practice icon

If A={1,2,3,4,5,6}, find C={xxA and x4}.

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Katrina
Katrina
Graham
Graham
Edwin espanol spanish
Edwin
Problem  8

Use the information in the Venn diagram to find the following sets.

  1. A

  2. B

  3. AB

  4. AB

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Molly S. cc
Molly S.
Logan
Logan
Cynthia espanol spanish
Cynthia
Problem  9
practice icon

Graph {xx2 or x>3}

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Anthony cc
Anthony
Betsy cc
Betsy
David espanol spanish
David
Problem  10

Graph {xx5 or x2}

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Molly S. cc
Molly S.
Logan
Logan
Cynthia espanol spanish
Cynthia
Problem  11
practice icon

Graph {xx>1 and x<2}

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David espanol spanish
David
Cynthia espanol spanish
Cynthia
Problem  12

Graph {xx>6 and x>3}

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Molly S. cc
Molly S.
Logan
Logan
Cynthia espanol spanish
Cynthia
Problem  13

Graph {xx2 and x4}

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Molly S. cc
Molly S.
Logan
Logan
Cynthia espanol spanish
Cynthia
Problem  14
practice icon

Solve and graph: 32x53

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Betsy cc
Betsy
Anthony cc
Anthony
David espanol spanish
David
Problem  15
practice icon

Solve 3t+74 or 3t+74

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Molly S. cc
Molly S.
Aaron cc
Aaron
Cynthia espanol spanish
Cynthia

6
Absolute Value Equations

Problem  1
practice icon

Solve |x|=5

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Mr. McKeague cc
Mr. McKeague
Brooke cc
Brooke
Aaron cc
Aaron
David espanol spanish
David
Problem  2
practice icon

Solve |2a1|=7

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Mr. McKeague cc
Mr. McKeague
Molly S. cc
Molly S.
David espanol spanish
David
Problem  3
practice icon

Solve |23x3|+5=12

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Ana
Ana
Aaron cc
Aaron
David espanol spanish
David
Problem  4
practice icon

Solve |3a6|=4

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Mr. McKeague cc
Mr. McKeague
Betsy cc
Betsy
Aaron cc
Aaron
Cynthia espanol spanish
Cynthia
Problem  5
practice icon

Solve |3a+2|=|2a+3|

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Ana
Ana
Aaron cc
Aaron
David espanol spanish
David
Problem  6
practice icon

Solve |x5|=|x7|

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Molly S. cc
Molly S.
Brooke cc
Brooke
Aaron cc
Aaron
David espanol spanish
David

7
Absolute Value Inequalities

Problem  1
practice icon

Graph |2x5|<3

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Mr. McKeague cc
Mr. McKeague
Brooke cc
Brooke
Anthony cc
Anthony
Edwin espanol spanish
Edwin
Problem  2
practice icon

Graph |3a+7|4

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Brooke cc
Brooke
Anthony cc
Anthony
Edwin espanol spanish
Edwin
Problem  3
practice icon

Graph |x3|>5

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Mr. McKeague cc
Mr. McKeague
Anthony cc
Anthony
Brooke cc
Brooke
Julieta cc espanol spanish
Julieta
Problem  4
practice icon

Graph |2x+3|+4<9

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Brooke cc
Brooke
Anthony cc
Anthony
Gordon espanol spanish
Gordon
Problem  5
practice icon

Graph |42t|>2

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Molly S. cc
Molly S.
Stefanie cc
Stefanie
Aaron cc
Aaron
Julieta cc espanol spanish
Julieta
Problem  6
practice icon

Solve |7y1|<2

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Molly S. cc
Molly S.
Betsy cc
Betsy
Octabio cc
Octabio
Cynthia espanol spanish
Cynthia
Problem  7
practice icon

Solve |6x+2|>5

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Betsy cc
Betsy
Aaron cc
Aaron
Cynthia espanol spanish
Cynthia
Mini Lecture

Mini Lecture
Solve and graph.

  1. |3y+9|6

  2. |3x+5|8<5

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Mr. McKeague cc
Mr. McKeague

8
Test & Summary

Problem  1

Solve: 547a=11

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Kendra cc
Kendra
Gordon cc
Gordon
Gordon espanol spanish
Gordon
Problem  2

Solve: 15x12110x+25=310x+12

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Kendra cc
Kendra
Gordon cc
Gordon
Gordon espanol spanish
Gordon
Problem  3

Solve: 5(x1)2(2x+3)=5x4

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Kendra cc
Kendra
Gordon espanol spanish
Gordon
Problem  4

Solve: 0.070.02(3x+1)=0.04x+0.01

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Kendra cc
Kendra
Gordon cc
Gordon
Edwin espanol spanish
Edwin
Problem  5

Solve for w: P=2l+2w

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Kendra cc
Kendra
Gordon cc
Gordon
Edwin espanol spanish
Edwin
Problem  6

Solve for B: A=12h(b+B)

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Kendra cc
Kendra
Gordon cc
Gordon
Edwin espanol spanish
Edwin
Problem  7

A rectangle is twice as long as it is wide. The perimeter is 36 inches. Find the dimensions.

Choose instructor to watch:
Gordon cc
Gordon
Problem  8

Two angles are supplementary. If the larger angle is 15 more than twice the smaller angle, find the measure of each angle.

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Gordon cc
Gordon
Problem  9

The longest side of a right triangle is 4 inches more than the shortest side. The third side is 2 inches more than the shortest side. Find the length of each side.

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Gordon cc
Gordon
Problem  10

Graph and solve: 5t30

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Gordon cc
Gordon
Problem  11

Graph and solve: 532x>1

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Gordon cc
Gordon
Problem  12

Graph and solve: 1.6x2<0.8x+2.8

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Gordon cc
Gordon
Problem  13

Graph and solve: 3(2y+4)5(y8)

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Gordon cc
Gordon
Problem  14

Solve: |14x1|=12

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Gordon cc
Gordon
Problem  15

Solve: |32x|+5=2

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Gordon cc
Gordon
Problem  16

Graph and solve: |6x1|>7

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Gordon cc
Gordon
Problem  17

Graph and solve: |3x5|43

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Joshua cc
Joshua
Lauren cc
Lauren
Gordon espanol spanish
Gordon
Problem  18

Graph and solve: |54x|7

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Gordon cc
Gordon
Kendra cc
Kendra
Problem  19

Graph and solve: |4t1|<3

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Kendra cc
Kendra
Gordon cc
Gordon