# Algebra 1 : Writing inequalities

## Example Questions

### Example Question #31 : Solve Word Problems Leading To Inequalities: Ccss.Math.Content.7.Ee.B.4b

Write the inequality:  Five less than a number is less than six.

Explanation:

Break up the sentence into parts.

Five less than a number:

Is less than six:

Combine the parts to make an inequality.

### Example Question #32 : Solve Word Problems Leading To Inequalities: Ccss.Math.Content.7.Ee.B.4b

Write the inequality:  The square root of twice a number is more than five.

Explanation:

Break up the sentence into parts.

Twice a number:

The square root of twice a number:

Is more than five:

Combine the parts to form the inequality.

### Example Question #33 : Solve Word Problems Leading To Inequalities: Ccss.Math.Content.7.Ee.B.4b

Write the inequality:  The difference of a number and six is more than forty.

Explanation:

Split up the sentence into parts.

Difference of a number and six:

Is more than forty:

Combine all parts to form the inequality.

### Example Question #41 : Linear Inequalities

Write the following inequality:  Two less than a number must be between negative two and negative four.

Explanation:

Start the problem by writing two less than a number.

This quantity must be between negative two and four, which includes both numbers.

The negative four will be smaller than negative two, which means that the number negative four will be on the left side of the inequality.

### Example Question #42 : Linear Inequalities

Write the inequality:  Sixteen less than three times a number is no less than five.

Explanation:

Split the sentence into parts.

Three times a number:

Sixteen less than three times a number:

No less than five means that the number cannot be less than five:

### Example Question #1 : Setting Up Inequalities

At a fair, there is a game where players step on a scale and weigh themselves. The objective of the game is for the host to guess the player's weight. A player loses if the host of the game can guess the player's weight within  pounds, inclusive. Suppose a player weighs  pounds. Write an inequality that represents the range of numbers such that the player loses. (Let  represent the guess weight.)

Explanation:

For the player to lose, the host has to guess within  pounds of the player's weight, inclusive. Thus, the host can guess any number between  pounds  and  pounds ; that is, if  is the weight the host guesses, then , which translates to

### Example Question #43 : Linear Inequalities

Write the inequality: The square of a number less than six is more than four.

Explanation:

Split the sentence into parts.

The square of a number:

The square of a number less than six:

Is more than four:

Combine the terms.

### Example Question #44 : Linear Inequalities

Write the following inequality:  A number less than two must be greater than four.

Explanation:

Break the sentence into parts.

A number less than two:

Must be greater than four:

Combine the terms to form the inequality.

### Example Question #45 : Linear Inequalities

Write the inequality:  Four more than twice a number is no less than eighty.

Explanation:

Break up the sentence into parts.

Twice a number:

Four more than twice a number:

Is no less than eighty:

Combine the terms.

### Example Question #46 : Linear Inequalities

Write the inequality:  Nine more than twice a number is at least fifteen.

Explanation:

Break up the sentence into parts.

Twice a number:

Nine more than twice a number:

Is at least fifteen:

Combine the terms to form an inequality.