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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.
 Absolute Value: Consider Two Cases [08/21/1997]

Could you please explain 7+3a = 11a ?
 Absolute Value Equations [10/30/2002]

What is the answer to 'the absolute value of x3 + the absolute
value of 3x = 12' ?
 Absolute Value Inequalities [06/23/2004]

I have to solve x + 3 < 5 and I don't remember if it's 'and' or
'or'. Is there an easy way to remember, or another way to solve the
problem?
 Absolute Value: Magnitude of a Number [11/24/1997]

Where is absolute value used in people's work?
 Absolute Value (Real Numbers: Rational) [02/02/1999]

Find the solutions of 1/(x2) >= 4.
 Absolute Value Sign [07/08/2003]

I understand how an absolute value works but when combined with order
of operation and signs I get confused.
 Absolute Value: Two Methods [07/03/1998]

Solve for x: x+3 < x2
 Adding and Subtracting Inequalities [09/29/1998]

Can you explain the rules? What if two inequalities are in the same or
opposite directions?
 Advanced Algebra [09/23/1997]

My teacher gave us this problem: 1+1/(1+1/(1+1/(1+1/1+...)))
 Algebra [5/10/1996]

Find the domain, range, and zeros of g(x)=x(squared)6x+4.
 Algebra as a Metaphor for Life [06/11/2002]

I've been given 'proofs' that 1 = 1, and that 2 > 4. Can you show me
why they aren't true?
 Algebraic expressions and fractions [04/10/1997]

If X/A+Y/B+Z/C = 1 and A/X+B/Y+C/Z = 0, what is
(X^2)/(A^2)+(Y^2)/(B^2)+(Z^2)/(C^2)?
 Algebraic Manipulation of Postfix Equations [05/14/2003]

Is it possible to solve a postfix equality algebraically, or does it
need to be converted back to infix notation?
 Algebraic Proof That a*0 = 0 [11/02/2003]

If 'a' is any element of all real numbers, then a*0 = 0. I would like
to understand the specific theorem or proof behind this idea.
 Algebraic Systems [09/07/1997]

Is * associative or commutative for the equation a*b = b h? for a*b =
ab+1?
 The Algebra of Complements and Supplements [01/25/1999]

What are complements and supplements? How do you translate these concepts
into algebra?
 Algebra PaperFolding Problem [02/10/1999]

Fold a paper x times in half, keeping the creases perpendicular to the
longest edge. Find an equation for the number of intersections in terms
of x.
 Algebra Puzzle [04/09/2001]

If x+y+z = 1 and x^2 + y^2 + z^2 = 2 and x^3 + y^3 + z^3 = 3, what does
x^4 + y^4 + z^4 equal?
 Algebra Refresher [12/31/1997]

I am trying to figure out how to solve this equation: (x^3 + 3x^2  4x +
3) / (x+1).
 Algebra Terms: 'Evaluate' and 'Simplify' [7/30/1996]

What do the terms "evaluate" and "simplify" mean in expressions like
"evaluate 3{23(27)}" or "simplify 3x{7(3x5)}"?
 The Algebra that High School and College Share in Common [12/05/2016]

In modern algebra, a teen does not recognize any of the algebra that he learned in
high school. Doctor Vogler emphasizes operations to explain the connection.
 All Possible Solutions: Diophantine Equations [12/06/2002]

Lance and Mario were working in the snack bar at the Turbulent Tunas
Concert. They sold hot dogs for $1.65, hamburgers for $2.35, sodas
for $.85, and the combo plate with fries, salad, a hamburger; and
soda for $3.89. They sold 80 items in an hour for $163.24. How many
of each kind of food did they sell, and how much did they make on
each kind of food?
 Alternative Formulas for Growth and Decay [08/02/2002]

I have two formulas for growth and decay: q = q_0*e^(rt), and q =
q_0*a^t. What is the difference between them?
 Analytical Solution [12/01/1997]

Can you give me an analytical solution of S[N] = Sum[k^2, {k,1,N}] ?
 Analyzing Range of Function with and without Calculus [08/19/2007]

Show that for all real values of x, the graph of (x^2 + x + 1)/(x + 1)
does not lie between 3 and 1 on the yaxis.
 Andy's Averaging Machine [6/23/1996]

How can Andy get a card with 3/32 on it? How can he get a card with 1/5
on it?...
 Angle Measurements of Triangles inside Semicircle [11/26/1998]

If the area of a triangle inside a semicircle is equal to the area
outside the triangle within the semicircle, then find the values of the
acute angles in the triangle.
 Ant and Rectangle [01/22/2001]

Does the ant walk along the diagonals of the rectangle?
 Applications of Parabolas [10/24/2000]

How are parabolas used in real life?
 Applying the Distributive Property to Division or Subtraction [12/29/2006]

The distributive property is easily shown with multiplication and
addition. Can it be used with subtraction or division?
 Applying the Remainder Theorem [10/25/1999]

If the expression 6x^2 + x + 7 leaves the same remainder when divided by
(xa) and by (x+2a) where a is not equal to 0, how can I find the value
of a?
 Approaching Asymptotes of Hyperbolas [04/24/2011]

Where do the equations for the asymptotes of hyperbolas come from? Doctor Peterson
derives them from a rigorous limit proof, starting with a definition of the term
"asymptote."
 Are (a)^3 and a^3 the Same Thing? [11/08/2005]

One question on a test I took was (a) * (a) * (a) = ?. I answered
(a)^3. My teacher said the answer is a^3 (same answer without the
parantheses). Aren't the two answers the same?
 Are All Functions Equations? [07/16/2001]

When my x's are not continuous, would I still have a function since the
vertical line test might in fact not touch a point at all?
 Area of an Inner Rectangle [01/19/2003]

Fred and Wilma's house had a 40 x 72 ft rectangular yard. Wilma
cultivated 5/12 of the area in flowers, which she grew in an
even border around the central grass area. Every morning Fred walked
Dino around the central grass area inside the flowers. How many laps
did he have to do to walk at least 1/4 mile?
 Area of a Right Triangle [02/09/2002]

Find the area of a right triangle that has a perimeter of length 16
meters and a hypotenuse with length 7 meters.
 Are These Properties of Real Numbers? [04/22/2002]

(a*b)/a=b; a(b)=a+b; a/b=a/b; a+(b)=ab; a^b*a^c=a^(b+c). They
all seem so intuitive we feel they must be properties.
 Arithmetic and Geometric Progressions [10/10/1995]

In an Arithmetic Progression, whose first term and common difference are
both nonzero, U(n) denotes the nth term and S(n) denotes the sum of n
terms. If U(6), U(4), U(10) form a Geometric Progression show that S(10)
= 0, show that S(6) + S(12) = 0, and deduce that U(7) + U(8) + U(9) +
U(10) = U(11) + U(12).
 Arithmetic Progression [12/19/1996]

If (b+ca)/a, (c+ab)/b and (a+bc)/c are in arithmetic progression, show
that 1/a, 1/b and 1/c are also in arithmetic progression.
 Arithmetic Sequence Conundrum [10/11/2002]

For some real number T, the first three terms of an arithmetic
sequence are 2T, 5T  1, and 6T + 2. What is the numerical value of
the fourth term?
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