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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(42x+y)  5x(y^2+xy)
 Simplifying Algebraic Expressions [6/20/1996]

a{2b+c2[d3a+e4]a2b3c5}afg(5ae3=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/x1))/(1+(1/x^21))
 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?
 SlopeIntercept 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 (x1)/(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 RateTimeDistance 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 = Mm/
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 <= 2x1 <= 15 for x?
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