# Algebra II : Setting Up Inequalities

## Example Questions

### Example Question #201 : Basic Single Variable Algebra

Set up the inequality:  Four times the quantity of two less than three times a number is at most ten.

Explanation:

Break up the inequality into parts.

Three times a number:

Two less than three times a number:

The quantity of two less than three times a number:

Four times the quantity of two less than three times a number:

Is at most ten:

Combine the terms to form the inequality.

### Example Question #202 : Basic Single Variable Algebra

Set up the following inequality:  The product of two and the quantity of two less than five times a number must exceed twelve.

Explanation:

Split up the inequality into parts.

Five times a number:

Two less than five times a number:

The quantity of two less than five times a number:

The product of two and the quantity of two less than five times a number:

Must exceed twelve:

### Example Question #203 : Basic Single Variable Algebra

Set up the inequality:  Twice the quantity of three less than twice a number must be more than ten.

Explanation:

Twice a number:

Three less than twice a number:

The quantity of three less than twice a number:

Twice the quantity of three less than twice a number:

Must be more than ten:

Combine the terms to write the inequality:

### Example Question #204 : Basic Single Variable Algebra

Set up the inequality:  Four less than six times the square root of a number is at least five.

Explanation:

Break up the statement into parts.

The square root of a number:

Six times the square root of a number:

Four less than six times the square root of a number:

At least five:

Combine the parts to form the inequality.

### Example Question #205 : Basic Single Variable Algebra

Set up the inequality:  Five more than eight times a number must exceed fourteen.

Explanation:

Separate the sentence into parts and let the unknown number be .

Eight times a number:

Five more than eight times a number:

Must exceed fourteen:

Combine the parts to form the inequality.

### Example Question #201 : Basic Single Variable Algebra

Set up the inequality:   Four less than eight times the square root of twice a number cannot be more than three.

Explanation:

Square root of twice a number:

Eight times the square root of twice a number:

Four less than eight times the square root of twice a number:

Cannot be more than three:

Combine the parts to form the inequality.

### Example Question #2052 : Algebra Ii

Set up the inequality:  Four less than twice a number is less than six times another number.

Explanation:

Let  be a number, and  be the other number.

Break up the sentence into parts.

Four less than twice a number:

Six times another number:

Less than:

Combine the terms to form the inequality.

### Example Question #2053 : Algebra Ii

Set up the following inequality:  Four less than twice a number is less than the eighty.

Explanation:

Set up the parts to form the inequality.

Twice a number:

Four less than twice a number:

Is less than eighty:

Combine the parts.

### Example Question #2054 : Algebra Ii

Set up the inequality:  Six less than twice a number squared must exceed eleven.

Explanation:

Break up the sentence into parts.

Twice a number squared:

Six less than twice a number squared:

Must exceed eleven:

Combine the parts to form the inequality.

### Example Question #2055 : Algebra Ii

Write the inequality:  Nine less than half a number squared is no greater than five.

Explanation:

Identify the parts of the inequality by breaking the sentence in parts.

Half a number squared:

Nine less than half a number squared:

Is no greater than five:

Combine the parts to form the inequality.