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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 an Equation with two Variables [11/20/1995]

The problem is n + n + 5 = 25. How do I do this? It has two variables.

Solving a Rational Inequality [11/15/2004]

How do you solve a rational inequality like (x-1)/(x+3) < 3?

Solving a System of Three Equations in Three Variables [06/23/2007]

How can I find values of x, y, and z that make all three of these equations true: x + y + z = 10, x - 2y + z = -2, and x - y - z = -12?

Solving a Typical Rate-Time-Distance Problem [09/02/2005]

A look at how to use algebra to solve problems involving rates, times, and distances. The problem in this example centers around walking and running at two different rates for a total of 3 hours.

Solving Equations [9/3/1995]

If n=x^2+y then how can you work out x if you know n and y, and work out y knowing n and x?

Solving Equations [3/23/1996]

A student has a number of 'word problems' that require solving equations.

Solving Equations [01/15/1998]

Please help me solve these equations: x2+y = 31; y2+x = 41.

Solving Equations for Variables [02/03/2002]

How do you solve the following equation for (M) and then (m)? k = M-m/ 1+Mm.

Solving Equations that Equal Zero [02/26/1997]

How do you solve an equation like (5x+10)(7x-2) = 0?

Solving Equations to Find Profit [8/10/1996]

You buy A and B for 40,000 Won; sell A for a 0.3 percent and B at a 0.2 percent discount. You profit 5000 Won - what was the original price of A?

Solving Equations with Square Roots [03/28/2003]

When solving x + 1 = sqrt(x + 3), we can square both sides then solve the equation; however, we get an extra solution that doesn't work. Why?

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 [12/10/1996]

How do you solve 6(m-4)-2(m+2) is less than 7(m-4)-6 ?

Solving Inequalities with a Balance Scale Analogy [08/31/1998]

How do you graph these inequalities...?

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 Inequalities: Picture a Number Line — or Several of Them ... [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.

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