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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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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?

Teaching Inequalities [04/01/2009]

We're looking for the best way to help students understand the idea of greater than or equal to, including some real-life examples of how it might be used. Do you have any thoughts?

Testing for Triangular Numbers [06/09/1999]

How do I figure out whether 12456, 1225, or 13456 are triangular or square numbers?

Thinking about the Mediant of Two Fractions [12/10/2009]

One of my students noticed that when given 1/a and 1/b, the fraction 2/(a+b) always seems to be in between 1/a and 1/b. Is this a new fraction rule, or has this been discovered and proved before?

Thirds of Seven [07/24/1997]

Seven is equal to how many thirds of seven?

Thoughtful Trial and Error [05/21/2002]

Arrange the numbers 1 through 10 in a triangle so that all the rows of three numbers have the same sum, and all the rows of four numbers have the same sum.

A Three-Legged Stool [06/26/2001]

Why is a three-legged stool steady, while a four-legged stool can be wobbly?

Three Less Than a Number [08/19/2001]

What is "three less than a number"? I believe it is x-3 but I am being challenged that it is 3-x.

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