Ask Dr. Math

High School Archive

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.

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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 [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 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 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 growth equations.

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?

Solving Systems of Three Equations [05/07/1998]

Can you help me solve the following system of three equations with three unknowns?

Solving x^3 + y^3 + z^3 [02/22/2003]

Given: x + y + z = 0; x * y * z = 2; x,y,z are not equal to each other; x,y,z all real numbers.

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