# High School Math : Basic Single-Variable Algebra

## Example Questions

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### Example Question #4 : Solving Inequalities

Solve the inequality for x:

Explanation:

Subtract 4 from both sides:

Divide both sides by 2:

### Example Question #5 : Solving Inequalities

Solve for .

Explanation:

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 :

Explanation:

Move like terms to the same sides:

Combine like terms:

Divide both sides by 3:

### Example Question #52 : Inequalities

Solve for :

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?

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)

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

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