High School Math : Basic Single-Variable Algebra

Study concepts, example questions & explanations for High School Math

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Example Questions

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Example Question #4 : Solving Inequalities

Solve the inequality for x:

Possible Answers:

Correct answer:

Explanation:

Subtract 4 from both sides:

Divide both sides by 2:

Example Question #5 : Solving Inequalities

Solve for .

Possible Answers:

Correct answer:

Explanation:

Add 4 to both sides.

Divide both sides by –7. When dividing by a negative value, we must also change the direction of the inequality sign.

Example Question #6 : Solving Inequalities

Solve for :

Possible Answers:

Correct answer:

Explanation:

Move like terms to the same sides:

Combine like terms:

Divide both sides by 3:

Example Question #52 : Inequalities

Solve for :

Possible Answers:

Correct answer:

Explanation:

Inequalities can be treated like any other equation except when multiplying and dividing by negative numbers. When multiplying or dividing by negative numbers, we just flip the sign of the inequality so that  becomes , and vice versa.

Example Question #1 : Understanding Direct Proportionality

Sarah notices her map has a scale of .  She measures between Beaver Falls and Chipmonk Cove.  How far apart are the cities?

Possible Answers:

Correct answer:

Explanation:

is the same as

So to find out the distance between the cities

Example Question #2 : Understanding Direct Proportionality

Sunshine paint is made by mixing three parts yellow paint and one part red paint. How many gallons of yellow paint should be mixed with two quarts of red paint?

(1 gallon = 4 quarts)

Possible Answers:

Correct answer:

Explanation:

First set up the proportion:

x =

Then convert this to gallons:

Example Question #3 : Understanding Direct Proportionality

If  is directly proportional to , and  when , find a formula for

Possible Answers:

Correct answer:

Explanation:

 since  and 

Solving for , you get that 

Replacing  in the original equation, you get the answer of 

Example Question #51 : Basic Single Variable Algebra

If  is inversely proportional to , and if  when , find a formula for

Possible Answers:

Correct answer:

Explanation:

Since y is inversely porportional to x, you can use the standard equations of  where k is a constant. Plugging the given x and y into this equation to solve for k, . To get the answer, substitute k into the standard equation. 

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