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Elementary Algebra
Linear Equations and Inequalities

1
Simplifying Expressions

Problem  1
practice icon

Simplify.

  1. \(3x+4x\)

  2. \(7a-10a\)

  3. \(18y-10y+6y\)

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Arielle cc
Arielle
Molly M. cc
Molly M.
Preston cc
Preston
David espanol spanish
David
Problem  2
practice icon

Simplify.

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

  2. \(4a-7-2a+4\)

  3. \(5x+8-x-6\)

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Arielle cc
Arielle
Molly M. cc
Molly M.
CJ cc
CJ
David espanol spanish
David
Problem  3
practice icon

Simplify \(5(2x-8)-3\)

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Arielle cc
Arielle
Molly M. cc
Molly M.
Preston cc
Preston
David espanol spanish
David
Problem  4
practice icon

Simplify \(7-3(2y+1)\)

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Stefanie cc
Stefanie
CJ cc
CJ
Arielle cc
Arielle
David espanol spanish
David
Problem  5
practice icon

Simplify \(5(x-2)-(3x+4)\)

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Arielle cc
Arielle
Molly M. cc
Molly M.
Preston cc
Preston
David espanol spanish
David
Problem  6
practice icon

Find the value of the expression \(2x-3y+4\) when \(x\) is \(-5\) and \(y\) is \(6\).

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Arielle cc
Arielle
Molly M. cc
Molly M.
Preston cc
Preston
David espanol spanish
David
Problem  7
practice icon

Find the value of the expression \(x^2-2xy+y^2\) when \(x\) is \(3\) and \(y\) is \(-4\).

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Arielle cc
Arielle
Molly M. cc
Molly M.
CJ cc
CJ
David espanol spanish
David
Problem  8

Substitute \(1, 2, 3,\) and \(4\) for \(n\) in the expression \(2n-1\)

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Arielle cc
Arielle
Molly M. cc
Molly M.
Preston cc
Preston
David espanol spanish
David

2
Addition Property of Equality

Problem  1
practice icon

Is \(5\) a solution to \(2x-3=7\)?

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Jesse cc
Jesse
Preston cc
Preston
David espanol spanish
David
Problem  2
practice icon

Is \(-2\) a solution to \(8=3x+4\)?

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Arielle cc
Arielle
Molly M. cc
Molly M.
Preston cc
Preston
Cynthia espanol spanish
Cynthia
Problem  3

Show that these sets of equations have the same solution set.

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Katrina cc
Katrina
CJ cc
CJ
Cynthia espanol spanish
Cynthia
Problem  4
practice icon

Solve \(x-5=12\)

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Arielle cc
Arielle
Preston cc
Preston
David espanol spanish
David
Problem  5
practice icon

Solve \(a+\displaystyle\frac{3}{4}=-\displaystyle\frac{1}{2}\)

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Aaron cc
Aaron
Molly M. cc
Molly M.
Preston cc
Preston
Anthony espanol spanish
Anthony
Problem  6
practice icon

Solve \(7.3+x=-2.4\)

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Mr. McKeague cc
Mr. McKeague
Preston cc
Preston
Arielle cc
Arielle
Cynthia espanol spanish
Cynthia
Problem  7
practice icon

Solve \(2x+2+2x=7+5\)

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Arielle cc
Arielle
Preston cc
Preston
Molly M. cc
Molly M.
Anthony espanol spanish
Anthony
Problem  8
practice icon

Solve \(4(2a-3)-7a=2-5\)

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Arielle cc
Arielle
Preston cc
Preston
Lauren cc
Lauren
Cynthia espanol spanish
Cynthia
Problem  9
practice icon

Solve \(3x-5=2x+7\)

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Lauren cc
Lauren
Preston cc
Preston
Molly M. cc
Molly M.
David espanol spanish
David

3
Multiplication Property of Equality

Problem  1

Solve: \(5x=30\)

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Nathan cc
Nathan
Claire cc
Claire
Breylor cc
Breylor
Octabio espanol spanish
Octabio
Problem  2
practice icon

Solve \(-4a=24\)

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Lauren cc
Lauren
Molly M. cc
Molly M.
Preston cc
Preston
Cynthia espanol spanish
Cynthia
Problem  3
practice icon

Solve \(-\displaystyle\frac{t}{3}=5\)

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Molly M. cc
Molly M.
Preston cc
Preston
David espanol spanish
David
Problem  4

Solve \(\displaystyle\frac{2}{3}y=4\)

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Molly M. cc
Molly M.
Lauren cc
Lauren
Preston cc
Preston
Cynthia espanol spanish
Cynthia
Problem  5
practice icon

Solve \(5+8=10x+20x-4x\)

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Jesse cc
Jesse
Preston cc
Preston
Anthony espanol spanish
Anthony
Problem  6
practice icon

Solve \(6x+5=-13\)

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CJ cc
CJ
Stefanie cc
Stefanie
Preston cc
Preston
Cynthia espanol spanish
Cynthia
Problem  7
practice icon

Solve \(5x=2x+12\)

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CJ cc
CJ
Stefanie cc
Stefanie
Preston cc
Preston
Cynthia espanol spanish
Cynthia
Problem  8
practice icon

Solve: \(3x-4=-2x+6\)

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CJ cc
CJ
Stefanie cc
Stefanie
Preston cc
Preston
Cynthia espanol spanish
Cynthia
Problem  9
practice icon

Solve \(\displaystyle\frac{2}{3}x+\displaystyle\frac{1}{2}=-\displaystyle\frac{3}{4}\)

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Preston cc
Preston
Betsy cc
Betsy
David espanol spanish
David
Problem  10
practice icon

Solve \(2(x+3)=10\)

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Mr. McKeague cc
Mr. McKeague
Arielle cc
Arielle
Matt cc
Matt
David espanol spanish
David

4
Solving Linear Equations

Problem  1
practice icon

Solve for \(x\): \(\:3(x-5)+4=13\)

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Mr. McKeague cc
Mr. McKeague
Matt cc
Matt
Cynthia espanol spanish
Cynthia
Problem  2
practice icon

Solve \(5(x-3)+2=5(2x-8)-3\)

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Mr. McKeague cc
Mr. McKeague
Molly M. cc
Molly M.
CJ cc
CJ
Cynthia espanol spanish
Cynthia
Problem  3
practice icon

Solve \(7-3(2y+1)=16\)

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

Solve \(3(2x-5)-(2x-4)=6-(4x+5)\)

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Mr. McKeague cc
Mr. McKeague
Arielle cc
Arielle
Matt cc
Matt
David espanol spanish
David
Problem  5

Solve: \(\dfrac{2}{3}x+\dfrac{1}{2}=-\dfrac{3}{4}\)

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Mrs. Mooney cc
Mrs. Mooney
Breylor cc
Breylor
Nathan cc
Nathan
Octabio espanol spanish
Octabio
Problem  6

Solve: \(\dfrac{1}{3}(x-4)+2x=\dfrac{3}{5}(4x+1)\)

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Nathan cc
Nathan
Claire cc
Claire
Breylor cc
Breylor
Octabio espanol spanish
Octabio
Problem  7
practice icon

Solve \(0.08x+0.09(x+2,000)=690\)

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Arielle cc
Arielle
Molly M. cc
Molly M.
CJ cc
CJ
David espanol spanish
David
Problem  8

Solve \(9a-2(3a+5)=3(a-1)-7\)

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Nathan cc
Nathan
Claire cc
Claire
Breylor cc
Breylor
Octabio espanol spanish
Octabio
Problem  9

Solve: \(\dfrac{1}{6}(5x+3)-\dfrac{1}{2}x=\dfrac{1}{3}(x-5)\)

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Nathan cc
Nathan
Claire cc
Claire
Breylor cc
Breylor
Octabio espanol spanish
Octabio

5
Formulas and Percents

Problem  1
practice icon

The perimeter \(P\) of a rectangle livestock pen is \(40\) feet. If the width is \(6\) feet, find the length.

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Betsy cc
Betsy
Molly M. cc
Molly M.
CJ cc
CJ
Cynthia espanol spanish
Cynthia
Problem  2
practice icon

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

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Molly M. cc
Molly M.
Betsy cc
Betsy
Preston cc
Preston
David espanol spanish
David
Problem  3
practice icon

Solve \(3x+2y=6\) for \(y\).

Choose instructor to watch:
Molly M. cc
Molly M.
Betsy cc
Betsy
CJ cc
CJ
Cynthia espanol spanish
Cynthia
Problem  4
practice icon

Solve \(h=vt-16t^2\) for \(v\).

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Betsy cc
Betsy
Preston cc
Preston
Anthony espanol spanish
Anthony
Problem  5
practice icon

Solve for \(y\): \(\displaystyle\frac{y-1}{x}=\displaystyle\frac{3}{2}\)

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Betsy cc
Betsy
Molly M. cc
Molly M.
Betsy cc
Betsy
Cynthia espanol spanish
Cynthia
Problem  6
practice icon

What number is \(25\%\) of \(60\)?

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Betsy cc
Betsy
Stefanie cc
Stefanie
CJ cc
CJ
Cynthia espanol spanish
Cynthia
Problem  7
practice icon

What percent of \(24\) is \(6\)?

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Betsy cc
Betsy
Preston cc
Preston
Aaron cc
Aaron
Anthony espanol spanish
Anthony
Problem  8
practice icon

\(45\) is \(75\%\) of what number?

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Betsy cc
Betsy
CJ cc
CJ
Cynthia espanol spanish
Cynthia

6
Applications

Problem  1
practice icon

The sum of twice a number and three is seven. Find the number.

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Betsy cc
Betsy
Molly M. cc
Molly M.
CJ cc
CJ
Edwin espanol spanish
Edwin
Problem  2
practice icon

One number is three more than twice another; their sum is eighteen. Find the numbers.

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Betsy cc
Betsy
Molly M. cc
Molly M.
Preston cc
Preston
Edwin espanol spanish
Edwin
Problem  3
practice icon

Bill is \(6\) years older than Tom. Three years ago Bill’s age was four times Tom’s age. Find their ages now.

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Betsy cc
Betsy
Molly M. cc
Molly M.
CJ cc
CJ
Edwin espanol spanish
Edwin
Problem  4
practice icon

The length of a rectangle is \(5\) inches more than twice the width. The perimeter is \(34\) inches. Find the length and width.

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Betsy cc
Betsy
Preston cc
Preston
Edwin espanol spanish
Edwin
Problem  5
practice icon

Jennifer has \(\$2.45\) in dimes and nickels. If she has \(8\) more dimes than nickels, how many of each coin does she have?

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Betsy cc
Betsy
CJ cc
CJ
Edwin espanol spanish
Edwin

7
More Applications

Problem  1
practice icon

The sum of two consecutive odd integers is \(28\). Find the two integers.

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Betsy cc
Betsy
Molly S. cc
Molly S.
CJ cc
CJ
Edwin espanol spanish
Edwin
Problem  2
practice icon

You invest money into two accounts. One account pays \(8\%\) annual interest and the other pays \(9\%\). You invest \(\$2000\) more in the account that pays \(9\%\) in annual interest. If the total interest earned at the end of the year is \(\$690\), how much is in each account?

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Betsy cc
Betsy
Molly S. cc
Molly S.
Preston cc
Preston
Edwin espanol spanish
Edwin
Problem  3

How much of a \(30\%\) alcohol solution and \(60\%\) alcohol solution must be mixed to get \(15\) gallons of \(50\%\) alcohol?

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Mrs. Mooney cc
Mrs. Mooney
Breylor cc
Breylor
Nathan cc
Nathan
Octabio espanol spanish
Octabio
Problem  4
practice icon

The angles of a triangle are such that one angle is twice the smallest angle, whereas the third angle is three times as large as the smallest angle. Find the measure of all three angles.

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Betsy cc
Betsy
Molly S. cc
Molly S.
CJ cc
CJ
Edwin espanol spanish
Edwin

8
Linear Inequalities

Study Skill

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

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Problem  2
practice icon

Solve \(x+5<7\)

Choose instructor to watch:
Stephanie cc
Stephanie
Preston cc
Preston
David espanol spanish
David
Problem  3
practice icon

Solve \(x-6 \leq -3\)

Choose instructor to watch:
Molly M. cc
Molly M.
Stephanie cc
Stephanie
Preston cc
Preston
Edwin espanol spanish
Edwin
Problem  4
practice icon

Solve and graph \(3a<15\)

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Stephanie cc
Stephanie
Preston cc
Preston
Edwin espanol spanish
Edwin
Problem  5
practice icon

Solve and graph \(-3a\leq 18\)

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Mr. McKeague cc
Mr. McKeague
Katrina cc
Katrina
CJ cc
CJ
David espanol spanish
David
Problem  6
practice icon

Solve and graph \(-\displaystyle\frac{x}{4}>2\)

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Mr. McKeague cc
Mr. McKeague
Katrina cc
Katrina
CJ cc
CJ
Edwin espanol spanish
Edwin
Problem  7
practice icon

Solve \(2.5x-3.48<-4.9x+2.07\)

Choose instructor to watch:
Katrina cc
Katrina
Betsy cc
Betsy
Preston cc
Preston
Edwin espanol spanish
Edwin
Problem  8
practice icon

Solve \(3(x-4)\geq -2\)

Choose instructor to watch:
Katrina cc
Katrina
Preston cc
Preston
Edwin espanol spanish
Edwin
Problem  9

Solve \(2(1-3x)+4<4x-14\), and graph the solution set.

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Stefanie cc
Stefanie
Preston cc
Preston
Edwin espanol spanish
Edwin
Problem  10
practice icon

Solve \(2x-3y<6\) for \(y\).

Choose instructor to watch:
Katrina cc
Katrina
CJ cc
CJ
Edwin espanol spanish
Edwin
Problem  11
practice icon

The sum of two consecutive odd integers is at most \(28\). What are the possibilities for the first of the integers?

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Preston cc
Preston
Stephanie cc
Stephanie
Edwin espanol spanish
Edwin