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Prealgebra
Solving Equations

1
The Distributive Property and Algebraic Expressions

Problem  1
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Simplify: \(-2(5x)\)

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Mr. McKeague cc
Mr. McKeague
Mrs. Mooney cc
Mrs. Mooney
Aaron cc
Aaron
Edwin cc espanol spanish
Edwin
Problem  2
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Simplify: \((2x+5)+10\)

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Mr. McKeague cc
Mr. McKeague
Mrs. Mooney cc
Mrs. Mooney
Aaron cc
Aaron
Anthony cc espanol spanish
Anthony
Problem  3
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Apply the distributive property: \(2(a-3)\)

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Mr. McKeague cc
Mr. McKeague
Mrs. Mooney cc
Mrs. Mooney
Matt cc
Matt
Edwin cc espanol spanish
Edwin
Problem  4
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Multiply: \(-4(3x+5)\)

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Mr. McKeague cc
Mr. McKeague
Arielle cc
Arielle
Aaron cc
Aaron
David cc espanol spanish
David
Problem  5
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Simplify: \(12x+3x\)

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Dr. Cavanah cc
Dr. Cavanah
Molly S. cc
Molly S.
Octabio cc
Octabio
Cynthia espanol spanish
Cynthia
Mini Lecture

Mini Lecture
Simplify.

  1. \(-6(3x)\)

  2. \(2+(3+x)\)

Multiply.

  1. \(2(6x-3y)\)

  2. \(5(7-4y)\)

Simplify.

  1. \((4x)^2(9xy)^2\)

Combine like terms.

  1. \(3x+5x\)

  2. \(6y-y\)

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Mr. McKeague cc
Mr. McKeague
Problem  7
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Simplify: \(5x-2+3x+7\)

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Matt cc
Matt
Stephanie cc
Stephanie
David cc espanol spanish
David
Problem  8
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Simplify: \(2(3y+4)+5\)

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Dr. Cavanah cc
Dr. Cavanah
Matt cc
Matt
Stephanie cc
Stephanie
David cc espanol spanish
David
Problem  9
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Simplify: \(2(3x+1)+4(2x-5)\)

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Arielle cc
Arielle
Aaron cc
Aaron
David cc espanol spanish
David
Problem  10
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Find the value of \(5a-12\) when \(a=2\)

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Molly S. cc
Molly S.
Octabio cc
Octabio
Cynthia espanol spanish
Cynthia
Problem  11
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Evaluate \(a(3-a)\) when \(a=-5\)

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Mr. McKeague cc
Mr. McKeague
Julieta cc
Julieta
Julieta cc espanol spanish
Julieta
Problem  12
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Find the complement of \(30^\circ\) and the supplement of \(45^\circ\)

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Mr. McKeague cc
Mr. McKeague
Julieta cc
Julieta
Aaron cc
Aaron
Julieta cc espanol spanish
Julieta
Mini Lecture

Mini Lecture
Combine.

  1. \(2x+8x\)

  2. \(4a-a\)

Simplify.

  1. \(4x+2x+3+8\)

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

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

  4. \(3(2a+4)+7(3a-1)\)

  5. Find the value of \(-4x+1\) when \(x=5\)

  6. Find the value of \(-a+10\) when \(a=-2\)

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Mr. McKeague cc
Mr. McKeague

2
The Addition and Subtraction Properties of Equality

Problem  1
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Is \(a=-2\) a solution to the equation \(7a+4=3a-2\)?

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Katrina cc
Katrina
Aaron cc
Aaron
Octabio cc espanol spanish
Octabio
Problem  2
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Solve the equation \(x-5=12\) for \(x\).

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Arielle cc
Arielle
Julieta cc
Julieta
Preston cc
Preston
Julieta cc espanol spanish
Julieta
Problem  3
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Solve for \(x\): \(\;3x-2-2x=4-9\)

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Mr. McKeague cc
Mr. McKeague
Aaron cc
Aaron
David cc espanol spanish
David
Problem  4
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Solve: \(\;4(2a-3)-7a=2-5\)

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Mr. McKeague cc
Mr. McKeague
Arielle cc
Arielle
Aaron cc
Aaron
David cc espanol spanish
David
Problem  5
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Solve for \(x\): \(\; x+4=-2\)

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Mr. McKeague cc
Mr. McKeague
Arielle cc
Arielle
Aaron cc
Aaron
David cc espanol spanish
David
Problem  6
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Solve for \(x\): \(\;-x+2+2x=7+5\)

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Mr. McKeague cc
Mr. McKeague
Julieta cc
Julieta
Julieta cc espanol spanish
Julieta
Problem  7
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Solve: \(10=-3y+2(5+2y)\)

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Mr. McKeague cc
Mr. McKeague
Julieta cc
Julieta
Julieta cc espanol spanish
Julieta
Mini Lecture

Mini Lecture

  1. Is \(x=-2\) a solution to \(2x+1=3x+3\)?

Solve.

  1. \(x-5=-4\)

  2. \(a+\dfrac{1}{3}=-\dfrac{2}{3}\)

  3. \(x+4-7=3-10\)

  4. \(8-5=3x-2x+4\)

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Mr. McKeague cc
Mr. McKeague

3
The Multiplication and Division Properties of Equality

Problem  1
practice icon

Solve \(\dfrac{x}{2}=3\) for \(x\).

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Mr. McKeague cc
Mr. McKeague
Julieta cc
Julieta
Julieta cc espanol spanish
Julieta
Problem  2
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Solve \(\dfrac{a}{3}+2=7\) for \(a\).

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Mr. McKeague cc
Mr. McKeague
Julieta cc
Julieta
Julieta cc espanol spanish
Julieta
Problem  3
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Solve \(4x=-20\)

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Julieta cc espanol spanish
Julieta
Aaron cc
Aaron
David cc espanol spanish
David
Problem  4
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Solve: \(-3x+7=-5\)

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Mr. McKeague cc
Mr. McKeague
Julieta cc
Julieta
Julieta cc espanol spanish
Julieta
Problem  5
practice icon

Solve: \(5x-8x+3=4-10\)

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Mr. McKeague cc
Mr. McKeague
Julieta cc
Julieta
Julieta cc espanol spanish
Julieta
Mini Lecture

Mini Lecture
Solve.

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

  2. \(3a=48\)

  3. \(-\dfrac{3}{5}x=\dfrac{9}{10}\)

  4. \(-4a+3=-9\)

  5. \(4x-7+2x=9-10\)

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Mr. McKeague cc
Mr. McKeague

4
Linear Equations in One Variable

Problem  1
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Solve: \(3(x+2)=-9\)

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Mr. McKeague cc
Mr. McKeague
Julieta cc
Julieta
Julieta cc espanol spanish
Julieta
Problem  2
practice icon

Solve: \(4a+5=2a-7\)

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Mr. McKeague cc
Mr. McKeague
Katrina cc
Katrina
Julieta cc
Julieta
David cc espanol spanish
David
Problem  3
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Solve: \(2(x-4)+5=-11\)

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Mr. McKeague cc
Mr. McKeague
Logan cc
Logan
Arielle cc
Arielle
David cc
David
Problem  4
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Solve: \(5(2x-4)+3=4x-5\)

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Mr. McKeague cc
Mr. McKeague
Julieta cc
Julieta
Arielle cc
Arielle
David cc espanol spanish
David
Study Skill
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Solve: \(\displaystyle\frac{x}{2}+\displaystyle\frac{x}{6}=8\)

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Mr. McKeague cc
Mr. McKeague
Matt cc
Matt
Arielle cc
Arielle
David cc espanol spanish
David
Study Skill
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Solve: \(2x+\displaystyle\frac{1}{2}=\displaystyle\frac{3}{4}\)

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Mr. McKeague cc
Mr. McKeague
Anthony cc
Anthony
Arielle cc
Arielle
David cc espanol spanish
David
Study Skill
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Solve: \(\displaystyle\frac{3}{x}+2=\displaystyle\frac{1}{2}\)

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Mr. McKeague cc
Mr. McKeague
Katrina cc
Katrina
Matt cc
Matt
David cc espanol spanish
David
Mini Lecture
practice icon

Mini Lecture
Solve.

  1. \(6(x-3)=-6\)

  2. \(7y-3=4y-15\)

  3. \(2(3x-6)+1=7\)

  4. \(9x-6=-3(x+2)-24\)

  5. \(\dfrac{x}{5}-x=4\)

  6. \(\dfrac{1}{x}-\dfrac{1}{2}=-\dfrac{1}{4}\)

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Mr. McKeague cc
Mr. McKeague

5
Evaluating Formulas

Problem  1
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Find the area and perimeter of a square with a side \(6\) inches long.

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Mr. McKeague cc
Mr. McKeague
Julieta cc
Julieta
Mrs. Mooney cc
Mrs. Mooney
Anthony cc espanol spanish
Anthony
Problem  2
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The perimieter \(P\) of a rectangular livestock pen is \(40\) feet. If the width \(w\) is \(6\) feet, find the length.

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Mr. McKeague cc
Mr. McKeague
Julieta cc
Julieta
Aaron cc
Aaron
Julieta cc espanol spanish
Julieta
Problem  3
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Use the formula \(C=\dfrac{5(F-32)}{9}\) to find \(C\) when \(F\) is \(95\) degrees.

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Mr. McKeague cc
Mr. McKeague
Winston cc
Winston
Octabio cc espanol spanish
Octabio
Problem  4
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Use the formula \(y=2x+6\) to find \(y\) when \(x\) is \(-2\)

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Mr. McKeague cc
Mr. McKeague
Lauren cc
Lauren
Aaron cc
Aaron
Julieta cc espanol spanish
Julieta
Problem  5
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Find \(y\) when \(x\) is \(3\) in the formula \(2x+3y=4\)

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Mr. McKeague cc
Mr. McKeague
Aaron cc
Aaron
David espanol spanish
David
Problem  6
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At \(1\) P.M. Jordan leaves her house and drives an average speed of \(50\) miles per hour to her sister’s house. She arrives at \(4\) P.M.

  1. How many hours was the drive to her sister’s house?

  2. How many miles from her sister does Jordan live?

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Dr. Cavanah cc
Dr. Cavanah
Katrina cc
Katrina
Aaron cc
Aaron
Julieta cc espanol spanish
Julieta
Problem  7
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Find the complement and supplement of \(25^\circ\)

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Arielle cc
Arielle
Aaron cc
Aaron
David espanol spanish
David
Mini Lecture

Mini Lecture
Let \(G=H\cdot R\) and find \(G\), if

  1. \(H=36\) hours and \(R=\$8\) per hour.

  2. \(H=20\) hours and \(R=\$6\frac{3}{4}\) per hour.

If \(C=\dfrac{5}{9}(F-32)\), find \(C\) if

  1. \(F=158\)

  2. \(F=32\)

If \(A=\pi r^2\), find \(A\) if \(\pi=\dfrac{22}{7}\) and

  1. \(r=7\) feet

  2. \(r=\dfrac{3}{4}\) feet

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Mr. McKeague cc
Mr. McKeague

6
Applications

Problem  1
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The sum of a number and \(2\) is \(8\). Find the number.

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Arielle cc
Arielle
Aaron cc
Aaron
David cc espanol spanish
David
Problem  2
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If \(5\) is added to the sum of twice a number and three times the number, the result is \(25\). Find the number.

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Anthony cc
Anthony
Julieta cc
Julieta
David cc espanol spanish
David
Problem  3
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The length of a rectangle is three times the width. The perimeter is \(72\) centimeters. Find its length and width.

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Arielle cc
Arielle
David cc
David
Julieta cc espanol spanish
Julieta
Problem  4
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The angles in a triangle are such that one angle is twice the smallest angle, while the third angle is three times as large as the smallest angle. Find the measure of all three angles.

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Katrina cc
Katrina
Aaron cc
Aaron
David cc espanol spanish
David
Problem  5
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Jo Ann is \(22\) years older than her daughter Stacey. In six years the sum of their ages will be \(42\). How old are they now?

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Dr. Cavanah cc
Dr. Cavanah
Matt cc
Matt
David cc espanol spanish
David
Mini Lecture

Mini Lecture

  1. The sum of a number and \(3\) is \(5\). Find the number.

  2. Three times the sum of a number and \(1\) is \(18\). Find the number.

  3. The length of a rectangle is twice its width. The perimeter is \(30\) meters. Find the length and width.

  4. Dale is \(4\) years older than Sue. Five years ago the sum of their ages was \(64\). How old are they now?

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Mr. McKeague cc
Mr. McKeague