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MIDDLE SCHOOL

About Math

Algebra
   equations
   factoring expressions
   graphing equations

Arithmetic
   division
   exponents
   factorials
   factoring numbers
   fractions/percents
   logarithms

Definitions

Geometry
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     conic sections/
       circles
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   3D and higher
     polyhedra

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Measurement
   calendars/
     dates/time
   temperature
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Number Sense
   factoring numbers
   negative numbers
   pi
   prime numbers
   square roots

Probability
Puzzles
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Browse Middle School Algebra
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    Direct and indirect variation.
    Inequalities and negative numbers.
    Positive/negative integer rules.
    Solving simple linear equations.



Solving for b [05/10/2000]
When solving 10 + 2*sqrt(b) = 0 we get b = 25, but when we insert 25 into the equation, we end up with 20 = 0. What are we doing wrong?

Solving for X [01/13/1997]
Solve for x in 3(x*x)-2x+2 = 2/(3(x*x)-2x+1).

Solving for x [1/23/1996]
I need help on this problem: x/x+4 = x+1/x+8

Solving for x with Fractions [9/9/1996]
How do I solve this: 5/2 = 3/2 - x ?

Solving Inequalities [08/31/1998]
How do you graph these inequalities...?

Solving Inequalities [12/10/1996]
How do you solve 6(m-4)-2(m+2) is less than 7(m-4)-6 ?

Solving Inequalities with Absolute Values [09/16/1998]
Can you explain two different ways to solve inequalities with absolute values?

Solving Linear Equations [03/18/1997]
What are the steps to solve linear equations?

Solving Linear Equations without PEMDAS [08/13/2002]
Is there a linear equation that can be solved using both the PEMDAS order of operations and NOT using the order of operations and still come out with the same answer?

Solving Linear Inqualities [06/10/1999]
How can I solve 9 <= 2x-1 <= 15 for x?

Solving Literal Equations [09/08/2001]
I can do equations fine with just numbers, but doing them literally with letters is confusing me.

Solving Pairs of Equations by Substitution [11/26/1997]
x + 3y = - 5; 3x - 2y = 7.

Solving Quadratic Equations [03/07/1997]
A rectangle has an area of 80 square units. Its length is one more than three times its width. What are the dimensions of the rectangle?

Solving Quadratic Equations [9/14/1996]
3x^2 + x - 14 = 0? x^2 - 6x + 8 = 0?

Solving Simple Equations [02/23/1998]
Equations like 3(30+s) = 4(s+19) and others following the same form.

Solving Single Variable Equations [02/02/1997]
How do you solve equations like 4g + 7 = 35?

Solving Systems of Equations Graphically and Algebraically [05/01/1998]
Graphing the system of equations y = -x and y = 2x, and indicating how many solutions it has.

Solving Systems of Linear Equations [02/09/1999]
Can you help me solve simultaneous equations?

Solving x-(-16) = 0 [02/17/1998]
How do you solve: x- -16 = -16?

Solving -X = 3 [10/26/1998]
How do you solve -X = 3? How can a negative equal a positive?

Speed of Two Trains [7/31/1996]
A train leaves Chicago for Indianapolis, 216 km away, at 9 a.m. One hour later, a train leaves Indianapolis for Chicago.... find the speed of each train.

Square Roots in Equations [06/12/1997]
When do you take the square root in: 2(x-4)^2 - 3 = 13 ?

Step-by-step Solution of Equation in One Variable [05/13/1998]
Commutative, associative, distributive, and other laws of arithmetic applied to solve w in the equation 2 - 2(w + 6) = 2(w + 5).

Straight Line on the Graph [09/10/1998]
Let f(x) = ae^(kx) where a>0 and k are constants. Show that the graph of y = ln(f(x)) is a straight line.

Strategy: Finding a Formula [11/14/1997]
Jill needs three pieces of lumber a total of 27 ft. long for a dog pen. The second piece has to be 4 ft. longer than the first and the third 4 ft. longer than the second...

Substituting Parameters for Numbers [11/29/2001]
I don't know what to do with both sides of the equation 17.20X/100 = X- 579.59.

Substituting Values for Variables [9/2/1996]
I know that a = -3/4 and b = -1/3. What's 2a+7b-ab/7a squared?

Substitution Method [01/08/2002]
Here is the problem: 2x+y = 3, 3x+2y = 5.

Subtracting as Adding a Negative [01/14/2002]
My teacher says to think of the question as a negative number, not a minus number, but I don't know how he's doing that.

Subtracting One Equation from Another [05/30/2001]
Why can you subtract one equation from another and get something meaningful that you can use to solve the equations?

Subtracting Taxes from Earnings [11/21/1995]
Customers at Flo's Meat Market must pay 6% state sales tax. One day Flo takes in $2650, including tax. How much of the $2650 does Flo have left after sending the tax money to the state?

Summing Three Consecutive Numbers [12/03/1998]
How many natural numbers from 10 to 40 can also be written as a sum of three consecutive natural numbers?

Sum of a Number and Its Reciprocal [01/28/2002]
The sum of a number and its reciprocal is 5 1/5. What is the number?

Sum of the Angles in a Star [09/21/1999]
How can I find the sum of the measures of the five acute angles that make up a star?

Sum of the Digits of Multiples of 9 [04/08/2001]
Why do the digits of nine times a single-digit number add up to 9?

The Sum of Two Numbers is 20... [11/03/1997]
Twice one number is 4 more than four times the other. Find the numbers.

Swimming Laps [04/15/2002]
John decides to swim a certain number of laps of the pool in five days. On the first day he covers one fifth of the total. The next day he swims one third of the remaining laps...

Swimming Upstream and Down [09/19/1997]
A man swims 200 meters upstream in 3 minutes (180 seconds) and downstream 150 meters in .7 minutes. How fast is the man swimming and how fast is the water?

Symbol for Integers [5/19/1996]
Why is the symbol for integers 'z'?

System of Equations and the Substitution Method [06/07/1998]
Can you explain the "substitution" method of solving systems of equations, and provide an example?

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