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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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/(x-2)| >= 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| < |x-2|

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 Paper-Folding 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-{2-3(2-7)}" or "simplify -3x{7-(3x-5)}"?

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 y-axis.

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 (x-a) and by (x+2a) where a is not equal to 0, how can I find the value of a?

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)=a-b; 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 non-zero, 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+c-a)/a, (c+a-b)/b and (a+b-c)/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?

Asking Price of a House [10/14/2001]

If a seller wants to clear $50,000 for his house and the real estate commission is 6%, what should be the asking price for the house?

Associative Property [5/22/1996]

What is the associative property in algebra?

Associative Property of Multiplication and Grouping Symbols [10/22/2006]

Does the Associative Property of Multiplication make grouping symbols unnecessary, since (a x b) x c = a x (b x c) = a x b x c?

Asymptote for (x-4)/x^2 [04/10/2002]

For the function (x-4)/x^2 there is a horizontal asymptote at y=0; however, at x=4 y=0 the graph of the function does intersect the line that is supposed to be the asymptote. How can this be if by definition the asymptote is a line that the function gets close to but does not touch?

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