See also the
Dr. Math FAQ:
order of operations
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.
Completing the square.
Direct and indirect variation.
Inequalities and negative numbers.
- 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-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
- 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/
- Solving Equations with Negative Coefficients [12/13/2005]
Two techniques for working with negative coefficients when solving
- 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 [01/19/1998]
How do you do these inequalities? x+1 > -2 and 3x < 6
- Solving Inequalities [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
- 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 with Absolute Values [05/31/1998]
Finding neighborhoods on the number line to solve 3 <= |x + 2| < 8.
- Solving Linear Inqualities [06/10/1999]
How can I solve 9 <= 2x-1 <= 15 for x?
- Solving Logistic Equations for a Variable in the Exponent [05/03/1998]
Using natural logarithms to solve for the time variable in two logisitic
- Solving Multivariable Diophantine Equations [05/03/1998]
Finding general solutions to two diophantine equations.
- 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 Quadratics with Imaginary Roots [05/28/1998]
Different ways to solve the quadratic equation 3x^2 + 2x + 5 = 0.
- Solving Rational Equations by Using the LCD [09/27/2007]
How do you solve the equation 3/(n-2) + 6/(n^2-5n+6) = 4/(n-3)?
- Solving Rational, Radical, and Polynomial Inequalities [12/28/2003]
I'm struggling with polynomial inequalities, such as (x - 2)(x + 3) >
0 or (x - 2)/(x + 3) < 2. I'm also not sure how to do inequalities
that have square roots in them. Can you help?
- Solving Sqrt(x + Sqrt(x + Sqrt(x + ... = 10 [02/26/2001]
How can I solve the equation sqrt(x+sqrt(x+sqrt(x+...=10 for x if x is
known to be a real number?
- Solving Systems of Equations [10/30/1996]
Solve for a, b, and c: 2a+6b+c = 5, a+b-c = -1, a+8b+2c = 0.
- Solving Systems of Linear Equations [02/09/1999]
Can you help me solve simultaneous equations?