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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.
 Natural Domain of a Function [03/12/1999]

Some inputs don't make sense for some functions.
 Natural Numbers Coprime to 6 [02/16/1998]

Let N(x) denote the number of natural numbers less than x which are
coprime to 6. Show that lim as x goes to infinity of [N(x)/x] = 1/3.
 Negative Exponents [10/23/1996]

I have to simplify this expression with nonnegative exponents: x^5.
 Negative Numbers Combined with Exponentials [03/09/2001]

Why in the order of operations is negation a multiplication done after
exponentiation, rather than as a part of the base? What about
polynomials?
 Negatives and Inequalities [09/10/1998]

Why when we multiply or divide an inequality by a negative number do we
reverse the inequality sign?
 Negative vs. Subtraction in Order of Operations [10/30/2002]

I am trying to find some definitive source for treatment of leading
negative numbers in simplifying with order of operations.
 Nested Negative Exponents [8/2/1996]

How do I deal with nested negative exponents?
 Net Result of Consecutive Percentage Increases [12/11/2003]

Suppose a quantity is increased by some percentage, and then is later
increased again by another percentage. How can I calculate the
overall percentage increase?
 Nonlinear Factors [10/12/1998]

I have been told that factoring the sum of two squared numbers is not
possible, but factoring x^4 + 4 is possible. Please explain.
 NonLinear Simultaneous Equations [12/07/2003]

I have four simultaneous equations with four variables, but each one
has a nonlinear term in it (e.g., ab + c + d = 3). So none of the
usual techniques will work! How can I solve the system?
 Normalization [08/01/2001]

How do I figure out: 90 + 70 + 88 + 94 + x / 5 = 85 ?
 The Nth Root of N [11/28/2000]

Is the nth root of n (a whole number other than 1) ever a rational
number?
 Number of Equations Needed in a Simultaneous Linear System [10/29/2003]

Could you tell me why we need the same number of equations as
variables in order to get a unique solution to a system of
simultaneous linear equations?
 Number * Sum of Remaining Four Numbers [04/03/2003]

Find 5 numbers such that when each number is multiplied by the sum of
the remaining 4 numbers, the following values will result: 152, 245,
297, 320, 360.
 Objects in a Pyramid [7/8/1996]

Objects are stacked in a triangular pyramid... how many objects are in
the nth layer from the top?
 Old Test Questions Answered [1/23/1995]

I am studying for my midterm, and I've come across two questions that I
got wrong and don't understand why....
 One Unknown, Decimal Power: By Inspection [10/18/2015]

An adult seeks to solve by hand for a variable raised to a decimal exponent. Doctor
Ali first simplifies the original equation to obtain its critical points and approximate its
maximum before reintroducing its factors and commenting on their effect.
 One Variable Equations with Decimals [02/11/1997]

How do you solve 8.25x + 3 = 17.5 + x?
 Open Sentence, Statement [09/18/2001]

What is an open sentence?
 Operator Precedence [08/13/2003]

Since the following statement is true: (1+1)**(52) is 8, why is the
following statement true and not false: 2**1+1 is 3 and not 4, and
3*1**3 is 3 and not 27...' ?
 Ordering Exponents and Variables [04/08/2000]

Is there a rule for putting terms in descending order if the variables
have the same exponent? What about negative exponents and descending
order?
 Ordering Products, Powers, and Parameters of Trigonometric Functions [10/31/2010]

A student wants to know how to unambiguously interpret strings of trigonometric
functions, multiplication, and exponentiation. Doctor Peterson digs into a history book
 as well as another math doctor's conversation  to illuminate the vagaries of the
notation.
 Order in Linear Expressions [11/20/2001]

Can you give me a convincing argument as to why, in an equation such as
y=137x, where y is a function of x, it should be written as y=7x+13?
 Order of Operations [05/19/1999]

Given a, b, x, and y, find ax/by.
 Order of Operations with Percentages [04/05/2001]

Why does the order of operations exclude percentage, square roots, etc.?
 Other Ways to Get the Quadratic Formula [02/19/2010]

Doctor Jacques shares two ways to derive [b +/ SQRT(b^2  4ac)]/2a
without explicitly completing the square.
 Pairs of Odd Integers [09/24/1997]

Find all pairs of odd integers a and b that satisfy the equation: a +
128b = 3ab.
 Parabola with Horizontal or Vertical Axis [05/03/2001]

How can I find the focus and directrix of a parabola whose axis is either
horizontal or vertical, like 2x^2 = y?
 Parabolic Golf Shot Equations [01/24/2002]

Does the ball reach the green?
 Parallel and Perpendicular Lines [01/14/1999]

How do you tell without graphing whether the graphs of these equations
are parallel, perpendicular, or neither?
 Parallel Lines [12/31/1998]

What are some ways of proving lines parallel  geometrically and
algebraically?
 Parametric Form for Equation of a Line [6/30/1996]

How can you convert an equation such as y = 3x/4 + 7/2 to parametric
vector form?
 Parity [8/2/1996]

How do I determine if the given function is odd, even or neither? What's
the symmetry of the graph?
 Partial Fractions [01/29/1998]

How do I express 3/1(x^3) in partial fractions?
 Pascal's Triangle Pattern [04/22/1999]

What pattern does multiplying each entry by 1, 2, 3, 4, 5... in order,
and adding the products yield?
 Perfect Square: Solving Two Equations [6/14/1996]

x^2 + 5 is a perfect square, and x^2  5 is a perfect square.
 Perimeter Equals Area in a Triangle [4/2/1996]

When will the area and perimeter of a right triangle be numerically
equal?
 Picture Frame, Triangle Measurements [5/20/1996]

My teacher gave us ten questions to answer and I could do all except two:
1) A framed rectangular picture is 35cm long and 25cm wide... 2) The base
of a triangle is 9cm more than the perpendicular height...
 Plus or Minus Sign [03/08/2002]

What does this equation mean: y = + k ? The  sign is directly under the
+ sign.
 Point Equidistant from 3 Other Points [04/11/1999]

How do you find a point that is equidistant from three other points?
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