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.
- The Importance of Defining Variables Clearly in Algebra [11/01/2007]
A sample of dimes and quarters totals $18.00. If there are 111 coins
in all, how many are there of each coin?
- Increasing the Average [02/25/2001]
Five members of a basketball team are weighed and an average weight is
recalculated after each weighing. If the average increases 2 pounds each
time, how much heavier is the last player than the first?
- Inequalities [08/01/1997]
How do I deal with an equation with a greater than or less than sign?
- Inequalities and Absolute Value - Case Method [09/01/1998]
What is the case method? How does it apply to inequalities with absolute
- Inequalities and Absolute Value: Examples with Solution Sets that Do and Do Not Intersect [10/17/1997]
What's the definition of absolute value?
- Inequalities and Absolute Value, with Emphasis on When Solutions Apply [8/28/1996]
How do I find the solution set for problems like |X| > X and
|X + 2| - X >= 0?
- Inequality Extraneity? [05/11/2017]
A teen wonders if, in multiplying both sides of an inequality by an unknown, he has
introduced extraneous solutions. By diagramming number lines with signs and
boundary points, Doctor Peterson outlines the consequences.
- Inequality with Absolute Value: What Does |x| Mean? [06/14/1999]
Why can't I just write the inequality |x| > a as (-a) > x > a?
- Infinite Geometric Progression [10/02/1997]
How do you go about solving .27 repeating into a fraction?
- Infinite sums [6/26/1996]
Given the function f(x) = x^2/(1+x^2) find the sum f(1/n)+f(2/n)+...+
f(n-1/n)+f(n/n) for any positive integers "N".
- Integer Solutions to AX + BY = C [04/25/2000]
How do you prove that, for any equation of the form ax + by = c, where a,
b and c are integers, if an integer solution exists, there will be an
infinite number of integer solutions for x and y?
- Intercept Equation [10/07/1998]
I found a plane using the intercepts (4,0,0), (0,-5,0), and (0,0,3). Now
I want an equation for those points using Ax + By + Cz = D.
- Intercept of Two Lines [06/07/1999]
How can you calculate the exact location of the intercept point of two
lines without graphing?
- Intercepts of Quadratic Functions [12/10/2003]
Why do some quadratic functions have two x-intercepts and one y-intercept?
- Interpreting Slopes [09/14/1998]
Does the graph of each of these equations rise to the right, fall to the
right, is it horizontal, or is it vertical?
- Intersecting Graphs [10/22/1996]
The graph of x^2 + xy + y^2 = 3 intersects the graph of x + xy + y
+ 1 = 0 in k distinct points. What is the value of k?
- Intersection Points [03/13/1999]
A line goes through the point A(1, 2) to cut 2y = 3x-5 at P and x+y = 12
at Q. If AQ = 2AP, find the coordinates of P and Q.
- Interval Notation [4/1/1996]
I need to learn about interval notation in terms of domain and ranges.
- Interval Notation [06/25/1997]
How do you express answers in interval notation?
- Interval Notation [11/01/1997]
Solve for x and write the answer in interval notation: -3 < -x < 2 / 3.
- An Introduction to Basic Diophantine Equations [08/27/2007]
A birdcage contains both 2-legged and 1-legged birds, and there are a
total of 11 legs in the cage. Use a Diophantine equation to find all
possible combinations of birds.
- Inverse Function [8/2/1996]
If z(x) = 4x + 15, what is the inverse of z(x)?
- Isosceles Triangle Maximizes Area? [09/11/2003]
How can you show that among all triangles having a specified base
and a specified perimeter, the isosceles triangle on that base has
the largest area?
- Is the Inverse a Function? [9/2/1996]
How do I find the inverses and determine whether the inverses are
- Is this Right? [1/9/1995]
How do you do a question like this: 2y(3y+1)-3(3y+1)+y(y+2)?
- Jack is Older than Jill [11/16/2001]
If you reverse the digits in Jack's age, you get Jill's age. The sum of
their ages equals 11 times the difference between them. Jack is older
than Jill. What are their ages?
- Lagrange Polynomial Interpolation [08/08/1997]
Please give me the definition and a brief example of how it works.
- Learning Algebra [03/02/1997]
I need a lot of help with Algebra!
- Length of a Copper Helix [11/15/1998]
Can you help me find a formula to determine the length of straight wire
needed to form a helix of a certain length when twisted with another
- Limits of Difference Equations [05/14/2000]
Find the limit of F and R in the following system of equations: R(x+1) =
a*R(x) - b*F(x) and F(x+1) = c*F(x) + d*R(x). This is similar to that of
the Lotka-Volterra ecological model.
- Linear Equations and Functions [10/11/1997]
The digits of a positive 2-digit integer N are interchanged to form an
integer K. Find all possibilities for N... the average of N, K, and 35 is
- Linear Inequalities [11/26/1997]
How do I solve the problem (x-2)/(x+1)<(x-4)/(x-1) ?
- Linear Systems [10/22/1996]
I need to solve this system of equations for x and y in terms of a, b, c,
d, e, and f: ax + by = e; cx + dy = f.
- Linear Systems of Equations in Two Variables [06/18/1999]
How can I find the length of AE, EB and DC, given that parallelogram ABCD
has a perimeter of 50, trapezoid AECD has a perimeter of 39, and AE = EC?
- Lines Intersecting Polygons [03/23/1998]
Given two points and polygons between them, if you draw a line between
the two points, how do you find which polygons it crosses?
- Logarithmic Problem [2/22/1995]
Can you help me solve this: log 3^x = 6 + (1/2)log 9^x?
- Logarithms and the Area of a Triangle [6/3/1996]
Is is true that if A is the area of a triangle, then....log(A) = ...?
- Looking for Patterns [10/30/2001]
What would be the answer to: (x-a)(x-b)(x-c)(x-d)(x-e)...(x-y)(x-z)?
- Lowest Integer That Can't Be Made [04/05/2004]
You have an unlimited number of 'a' cent stamps and 'b' cent stamps, where both a
and b are relatively prime positive integers. I am interested in finding a postage value above which any postage amount can be made. I need to find a formula involving a and b, that will give the cutoff point for any such pair of numbers a and b.
- Magic Wheel [03/20/2002]
Given a wheel with 16 spokes and a hub, enter the whole numbers 1-17 in
the hub and at the end of spokes. The sums of the 3 numbers along the
spokes must be equal.