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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Rational Inequality [10/09/2001]

Solve this rational inequality and give an answer in interval notation: - 5/(3h+2) greater than or equal to 5/h.

Real and Complex Equations [09/21/1998]

I'm having trouble simplifying some real and complex equations for Algebra II. Can you help?

Regrouping Polynomials [11/19/2001]

I'm stuck on problems like a^2x - bx - a^2y + by + a^2z - bz.

Renting Bike Safety Equipment [10/09/2001]

The Park Department rents a bike with safety equipment for $5 a day. If you provide your own safety equipment, the bike rental is $3 a day. You could buy equipment at a sports store for $28. How many times must you use the trail to justify buying your own safety equipment?

Representing Numbers in Different Bases [08/05/1998]

How did they get the 2 x 3 cubed? Plus some number less than 3 cubed?...

Silver Alloy [07/12/2001]

Sterling Silver is 92.5% pure silver. How many grams of pure silver and sterling silver must be mixed to obtain 100g of a 94% Silver alloy?

A Simple Formula? [02/21/1997]

If one person takes two hours to paint a wall and another only one hour, how long will it take them to paint the wall together?

Simplifying Algebraic Expressions [03/23/2002]

Please explain how to simplify algebraic expressions.

Sketch an Equation [10/07/1997]

How do I rearrange -3x+2y = -6 to sketch it?

Solving Inequalities [9/8/1995]

Can you help me with this problem? 1 is less than or equal to (4 - 5K) is less than 9.

Solving Quadratic Equations [5/23/1996]

5x+x(x-7)= 0

Solving Simultaneous Equations and Factoring [3/18/1996]

Vanessa built a rectangular pen for her dogs. She used an outside wall of the garage for one of the sides of the pen. She had to buy 20m of fencing...

Solving the Quartic [05/27/1998]

Can you show me how to solve quartic equations directly?

Stairs on an Escalator [05/21/2001]

A woman walks 10 steps down on a downward-moving escalator to reach the bottom. As she reaches the bottom, she runs back up the same escalator at a speed 5 times that which she walked down, covering 25 steps in reaching the top. How many steps are visible on the escalator when it is still?

Substituting in Linear Equations [11/14/2001]

I am given two equations, 2y = 5x + 8x and 3y = 4x + 9x, and told to substitute something. What should I do?

Train, Distance, and Speed [09/20/1997]

How fast does Bobo run?

Transformations [12/14/1995]

A 10th grade student asks Dr. Math to check a problem concerning transformations.

Two Methods of Factoring Quadratics [04/14/1998]

Could you describe how to factor quadratic trinomials?

Unions and Intersections [2/9/1995]

In my text, there are these upside-down horseshoe looking things, and there is no explanation of what they are or why they exist...

Unsolvable Equations [11/10/2001]

If I have an equation in the form of x^n+y^n=z, how do I solve for n?

Unsolvable Equations, Feedback Loops, Existence Proofs... [04/14/1997]

How do you solve equations like (9/4)^x = x^(9/4) ?

Upstream and Downstream Speed [08/16/1998]

It takes a ferryboat 2 hours to travel 30 miles going downstream and 3 hours for the return trip upstream. What is the ferryboat's speed in still water?

What Are Quadratic Functions? [02/27/2003]

What is the difference between a quadratic function and a quadratic formula?

What is a Quadratic Equation? [08/04/1997]

What is a quadratic equation? What is it used for? How can we use it to solve everyday problems?

What is Slope? [9/2/1996]

What is a slope, and if given a slope = n equation, how do you apply that slope number to another graph problem?

When do the Cars Meet? [01/23/1997]

Two cars are 635 kilometers apart. They start at the same time and drive toward each other. One travels at 70 km/h and the other travels at 57 km/hr. In how many hours do they meet?

Which Barrel is Unsold? [3/1/1995]

There are six barrels with volumes of 8, 13, 15, 17, 19, and 31 litres respectively. These barrels contain either petrol or diesel oil. The price of petrol is twice the price of diesel oil per litre...

Write in Slope-Intercept Form [11/06/1997]

Write and sketch x - y + 2 = 0 .

X greater than 25, OR less than 30 [8/17/1996]

x > 25 or x < 30. The "or" part of the problem bugs me. Is the answer {26, 27, 28, 29}?

10% Sodium + 30% Sodium [07/09/2003]

A group of chemists are conducting an experiment to produce a new liquid material. One chemical contains 15% sodium (Na) and the other chemical contains 30% sodium (Na). Once they mix the two samples the resulting chemical contains 22% sodium (Na). How many milliliters (ml) of each sample must be mixed to obtain 600 ml of the new chemical?

14b * 20x Rearranged [03/11/2002]

What is 14b times 20x ?

24 Factors [12/08/1996]

What is the smallest positive integer with exactly 24 different positive factors?

300 Foul Shots [07/11/2001]

A basketball player shoots 100 foul shots on a given day, and increases the number he shoots by 10 per day...

33 Pearls Problem [11/14/1996]

On a string of 33 pearls, the middle pearl is the most expensive one - find its value.

4-Variable Systems of Equations [12/10/2002]

2w-x+5y+z=-3; 3w+2x+2y-6z=-32; w+3x+3y-z=-47; 5w-2x-3y+3z=49.

9 x HATBOX = 4 x BOXHAT [05/30/2000]

What is the solution to the cryptogram: 9 x HATBOX = 4 x BOXHAT?

Absolute Value and the Distributive Property [12/11/2001]

Is the distributive property applicable to absolute value?

Absolute Value As Statement about Distance [10/16/2002]

|x|+|x+2|+|x-4| < 5.

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

Could you please explain |7+3a| = 11-a ?

Absolute Value Equations [10/30/2002]

What is the answer to 'the absolute value of x-3 + the absolute value of 3-x = 12' ?

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