7-2 Solving Inequalities

Drill #103

Write an inequality for each sentence below:

1. Three times a number is greater than ten plus that number.

2. 8 less than twice a number is less than three times that number.

3. The sum of four and a number is less than or equal to the quotient of five and that number.

Less than, is less thanGreater than, is greater than

Eight less than twice a number is less than five.

Twelve more than a number is more than ten times the number squared.

Writing Inequalities in Word Problems

Write an inequality that represents the following situation:

Allen Iverson scored 25 points against Seattle last night. If 8 of his points were free throws, at most what number of 3 point baskets could he have made?

*Inequalities

< > < >•Is less than•Is fewer than

•Is greater than•Is more than

•Is at most•Is no more than•Is less than or equal to

•Is at least•Is no less than•Is greater than or equal to

*Graphing Inequalities on a Number Line

• Greater than and less than:

x > 5 x is greater than 5

x < 3x is less than 3

Draw a circle around the point on the number line. Draw a line from the circle to the end of the number line (to the right for greater than, to the left for less than)

Graphing Inequalities on a Number Line

• Greater than or equal to and less than or equal to:x > 5 x is greater than or equal to5

x < 3x is less than or equal to 3

Put a point on the number line at the number. Draw a line from the point to the end of the number line (to the right for greater than, to the left for less than)

Identity and No Solution

• When all the variables drop out of an inequality the solution is either:

– No Solution (if the statement is false)– The Identity (if the statement is true)

Classwork #103

Solve the following inequalities,

Decide whether no solution or the identity results:

1. 3x + x < 4x + 2

2. 3 (x + 1) > 3x + 5

3. 5 – 3 + x > x + 2

Drills and Quizzes

There will no longer be drill quizzes. Quiz problems will be taken directly from the drills.

Do your drills so you will do well on your quizzes.

Classwork 7-2

• Do the odd problems on Study Guide 7-2.

• Do the even problems for homework.