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Middle School Archive

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.

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Factoring a Polynomial [04/06/1997]

How do I solve 3y^2+12y = 0?

Factoring a Quadratic with Fractions [10/08/1999]

How can I factor x^2 + (1/2)x + (1/16)?

Factoring a Sum of Squares [10/15/2005]

I do not understand why you cannot factor a sum of two squares, but you can factor a perfect square trinomial.

Factoring a Trinomial [08/26/1997]

How do you reduce 5k^2-13k-6 / 5k+2 to lowest terms?

Factoring a Trinomial [08/22/2003]

What is factoring by grouping? When factoring a trinomial, why is it necessary to write the trinomial in four terms?

Factoring by Grouping [05/27/1998]

How do you factor 2r^2 + rt - 6t^2 ?

Factoring by Grouping to Solve a Polynomial Equation [05/26/2005]

How do I solve an equation like x^3 + 3x^2 - x - 3 = 0 by factoring? I'm having trouble factoring because of the four terms and the x^3.

Factoring Polynomials [11/29/1999]

How can I factor 4x^2 - 36, or x^2 + yz + xy + xz?

Factoring Problems [8/14/1996]

What is the width of an uniform border surrounding a rectangle?

Factoring Quadratics When a Doesn't = 1 [03/24/2003]

A trick to solving quadratics was presented to me. I was wondering if there is a proof for it.

Factoring to Solve a Problem [7/31/1996]

I have problems understanding the solution I get when I factor an expression to solve: x (x + 1) = 132...?

Factoring Trinomials by the Grouping Method [12/08/2005]

A discussion and proof of why factoring trinomials by grouping works.

Factoring vs. an Equation [10/01/2002]

The product of two consecutive odd numbers is 255. Find the numbers.

Factoring vs. Simplifying [03/02/2003]

Factor the expression 1+y(1+x)^2(1+xy).

Factoring (x - 1)(x^2 - x - 2) [11/04/1997]

I don't remember how to factor.

Farmer Buying Livestock [9/12/1996]

A farmer spends $100 total to get 100 animals. Cows are $10, pigs $3, chickens $0.50...

Faster Than Algebra [05/14/2002]

The sides of a rose garden in the shape of a right triangle are in a ratio of 8:15:17. If the perimeter is 60 feet, what is the length of the shortest side?

Filling a Tank [08/01/1997]

How long will it take two pipes together to fill a tank?

Filling a Tank [12/19/2002]

A tank is filled by two pipes. The smaller pipe alone will take 24 minutes longer than the larger pipe and 32 minutes longer than when booth pipes are used. How long will each pipe take to fill the tank alone?

Find a Counterexample [8/29/1996]

What is a counterexample for the statement: if a > b and b = 5, then a >= 6.

Finding a Formula for a Number Pattern [09/30/2004]

We are learning about sequences and how to find the patterns in numbers. Our teacher gave us the sequence 0, 3, 8, 15, 24, 35 and told us that we had to use factoring to find the answer. I know the answer is (n + 1)(n - 1), but I can't see how to get that.

Finding a Formula for Mixtures [11/10/2003]

Alfredo needs to make 250 ml of a 27% alcohol solution, using a 15% solution and a 40% solution. How much of each should he use?

Finding a Fraction that Equals an Unending Number [07/08/2003]

Is there a way to find if there is a fraction that equals 0.777777...?

Finding Ages: Tot and Teen [12/01/2002]

Tot is now half as old as Teenager was when Tot was a third as old as Teenager is now.

Finding a Set, Solving a System [06/24/1998]

Find the solution set: 3-1/4x <_ 2+ 3/8 x; solve the system...

Finding a Single Pair of Factors [02/27/2002]

Factor ax^2 - bx - c.

Finding Least Common Multiple for Day Problem [01/14/2004]

Club A meets every 7 days. Club B meets every 10 days. How often will the clubs meet on the same day?

Finding Line Segment Lengths [12/21/2001]

Can you help me find line segments AB and BC if points A,B,C, and D are collinear with B between A and C and C between B and D...?

Finding Original Amount before a Percent Was Added [04/24/2007]

If I paid $25.00 for gas and that includes 42% in taxes, what was the cost of the gas before the taxes?

Finding Rules for Number Patterns [06/05/2009]

I'm having trouble finding an algebraic expression that generates the pattern 3, 5, 8, 12, 17, 23, 30. Can you help?

Finding the Difference of the Cubes of Two Numbers [9/29/1995]

The difference of two numbers is 1. The product of the two numbers is also 1. What is the difference of the 2 numbers cubed?

Finding The GCF and LCM of Terms with Variables [08/25/1999]

How do you multiply terms with variables that have exponents? How can you find the GCF or LCM of such terms?

Finding y-intercepts [6/12/1996]

I'm having a problem with finding and graphing y-intercepts of linear equations.

Find Quadratic Equation From Roots [9/15/1996]

Write a quadratic equation with roots: -4 +/- sqrt(10)

Find the Number [05/14/1997]

Five times a certain number is six less than three times the same number. What is the number?

Find X [01/22/2001]

Use your knowledge of powers and the properties of exponents to find the value of x in the equation 8^x+2=2.

First Year Algebra [6/19/1996]

What should a person have learned after one year of Algebra I? I want to be prepared for Geometry next year.

Fitting a Picture to a Frame [11/14/1996]

I have a picture frame that needs to have twice as much border on the side of the picture as on the top. If the photo is half the area of the frame, how wide should the borders be?

Five Bags of Nuts [04/17/2002]

Given 100 nuts in five paper bags, in the first and second bags there are altogether fifty-two nuts; in the second and third there are forty-three; in the third and fourth, thirty-four; in the fourth and fifth, thirty. How many nuts are there in each bag?

Formulas and Missing Quantities [10/09/2004]

Variations on the question "Could you drink enough water in a lifetime to empty a pool?" lead to a discussion of using formulas to find missing quantities.

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