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Browse High School Basic Algebra
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    Solving simple linear equations.
    Positive/negative integer rules.
    Mixture problems.
    Quadratic equations.
    Absolute value.
    Completing the square.
    Direct and indirect variation.
    Inequalities and negative numbers.

Ships in the Fog [02/01/1999]
Given the locations and speeds of two ships, find whether (and when) they will collide.

Sign Switching [01/28/2002]
Can you explain sign switching in multiplying and dividing inequalities?

Simple Way to Solve an Iterative Equation? [01/09/2009]
Bonuses are paid based on the percentage of projected profitability attained. But the bonus payment in turn reduces the profitability, which reduces the bonus. Through a series of iterations the amounts eventually converge, but is there a simple way to determine the bonus amount without having to go through those iterations?

Simplification [05/04/1997]
Which is more simplified: (1/a) + (1/b) or (a+b)/ab?

Simplification Problems [8/20/1996]
Simplify 2x(4-2x+y) - 5x(y^2+x-y)

Simplifying Algebraic Expressions [6/20/1996]
a-{2b+c2[d-3a+e4]a2b3c5}afg(5a-e3=cd3)2f+4g+f9 = ?

Simplifying Equations [11/7/1995]
Simplifying a fractional equation.

Simplifying Equations [4/11/1996]
I need to solve this by factoring, finding the lowest common denominator, then multiplying by the reciprocal. Simplify: (1+(1/x-1))/(1+(1/x^2-1))

Simplifying with Cube Roots [01/22/1997]
Simplify: cube root(3) / [cube root(6) + cube root(3)]

Simultaneous Equations [11/28/1995]
A student asks about solving simultaneous equations.

Simultaneous Equations [07/01/2002]
A man has a total of 20 dimes and quarters. If the dimes were quarters and the quarters were dimes he would have 90 cents more than he has now. How many of each coin does he have?

Simultaneous Equations and the Addition Method [06/01/1998]
Solving two unknowns in two equations.

Slope and (x, y) Intercept [02/19/1999]
Does slope depend on (x, y) intercept or does (x, y) intercept depend on slope?

Slope-Intercept Formula [06/05/2001]
Why does y = mx + b have to be that way?

Solutions to X^Y = Y^X [12/21/2000]
How can I find the solutions to the equation x^y = y^x? I have been told that it involves the Lambert W Relation.

Solve for X Algebraically [07/24/2003]
Solve for x algebraically, (no graphing): 2^x + 2^(-x) = 5.

Solve It Numerically [05/21/1997]
How do you solve the equation x^x = 100?

Solving Absolute Value Equations [01/12/2004]
How do I solve an absolute value equation with variable expressions on each side, such as abs(x + 1) = abs(x - 1)?

Solving Absolute Value Functions [07/19/1998]
How do you solve |4/7x + 6| + 3 = 15?

Solving a Complicated Equation [4/25/1995]
Please solve this equation for variable X with parameter k: sin(X) + sin(5*X) + sin(9*X) + ... + sin((4*k+1)*X)=k+1

Solving a Diophantine Equation [01/28/2005]
Solve the following Diophantine equation: 5x + 3kx = 8k^2 - 25

Solving a Math Poem [05/24/2000]
Take five times which plus half of what, and make the square of what you've got...

Solving an Inequality [6/17/1996]
6/(2X+1) > (1/X) (1+log2 (2+X))

Solving a Quartic Equation with Substitutions [11/02/2004]
I'm trying to solve y(y + 1)(y + 2)(y + 3) = 7920. I've multiplied it out to get y^4 + 6y^3 + 11y^2 + 6y - 7920 = 0, but I can't find a way to factor or solve that equation. Can you help?

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 for Variables [02/03/2002]
How do you solve the following equation for (M) and then (m)? k = M-m/ 1+Mm.

Solving Equations with Negative Coefficients [12/13/2005]
Two techniques for working with negative coefficients when solving algebraic equations.

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 Rate [8/8/1996]
In the equation P=V*R/(1-(1+R)^(-n)), how do you solve for "R"?

Solving for Variable [2/7/1996]
Given the equation P=V*R/(1-(1+R)e^(-N)), how is this simplified to solve for R (rate) if Pt, PV, and N are known?

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

Solving Fractional Systems of Equations [06/08/1998]
I need help solving the following system of equations - the fractions have confused me: 1/x + 3/y = 7 and 4/x -2/y = 1.

Solving Inequalities in Phases and Shadings [01/19/1998]
How do you do these inequalities? x+1 > -2 and 3x < 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 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?

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