J3 Solving Linear Inequalities in One Variable

Embed Size (px)

Citation preview

J3 Solving linear inequalities in one variable (the first lesson of a unit on inequalities) Students individually solve a word problem in various ways, and then the teacher selects individuals to come to the board to present solutions to the class (the teacher determines the order of presentation). Solution methods include: counting objects, using a table, solving the problem arithmetically, using a linear equation, and using a linear inequality. Students then use linear inequalities to solve another problem. J4 Solving linear inequalities in one variable (the seventh lesson of a unit on inequalities) Students come to the board to write homework solutions. The teacher poses a word problem, students work on it individually, and then two students and the teacher present solutions (the teacher determines the students and the order). Solution methods are: guessing and checking, using arithmetic, and representing the problem as an inequality. The teacher then poses two related problems. Students work on these individually, and then two students come to the board to write their solutions, which use inequalities.

Let's quickly recap some of the steps for solving inequalities. Solve the inequality as you would an equation. If you multiply or divide by a negative number, REVERSE the inequality symbol. Use an open circle on the graph if your inequality symbol is greater than or less than. Use a closed circle on the graph if your inequality symbol is greater than or equal to OR less than or equal to.

Directions: Solve each inequality and graph the solution. Click here to print out number lines for your practice!

Answer Key

Problem 1

Problem 2

Word Problem Solving Strategies Read through the entire problem. Highlight the important information and key words that you need to solve the problem. Identify your variables. Write the equation or inequality. Solve. Write your answer in a complete sentence. Check or justify your answer.

Inequality Key Words at least - means greater than or equal to no more than - means less than or equal to more than - means greater than less than - means less than

Example 1

Example 2

Are you ready to practice inequalities by solving these word problems? Yes... I do know the answer by now - but - I know you can do it! Now, I want you to prove it to yourself! Let's quickly recap a few things and you'll be on your way! Let's keep these key words for inequalities handy: at least - means greater than or equal to no more than - means less than or equal to more than - means greater than less than - means less than

Work through each problem slowly and start by identifying your variables! Ok... get to work!

Practice Problems

Answer KeyProblem 1

Problem 2

1.

Solve: 3x - 7 < 2Top of Form

A ns w erBottom of Form

2.

Which of the following is the graph of:Choose one:

y

4

Top of Form

a.

a b cBottom of Form Top of Form

b.Answ erBottom of Form

c. 3. Solve: 2x - 5 > x - 2Answ erBottom of Form Top of Form

4.

Solve:

2 - 5x

3x - 14Top of Form

Answ erBottom of Form

5.

Which of the following is the graph of:

x > -2Top of Form

Choose one:

a.

a b c dBottom of Form

b.Top of Form

c.

Answ erBottom of Form

d.

6.

Solve: 2(y + 1)

y-4Top of Form

Answ erBottom of Form

7. Which value of x is in the solution set of the inequality: -2x + 5 > 17 ?

Choose one:Top of Form

-8 -6 -4 12Bottom of Form

Cryptic Cubes are a good way to relieve some of the monotony associated with drill and practice.

Below you will find a sample set of cubes which could be used with your class for practice on solving equations and inequalities. For more information on making cryptic cubes, see the "Cryptic Cubes" page.

Make, or have your students make, sets of 3 cubes like the ones below. You can pair students up and have them work as partners or have them work individually.

x+7 2(x + 4)

2x - 3 5 - 2x

4x - 1 x-3

4(2 - x) 8-x

5x - 3 3(x + 1)

3x - 5 -5

Answer the following questions dealing with inequalities. 1.

The community basketball team is pictured above. Can you determine the height of each player?

Answer

2.

(graphical information from CORD Math)

The graph above can be used to locate safe and unsafe speed zones. The lower shaded region is a safe-speed zone where d < 55t. (d is less than 55t for any pair (t, d) in this region) The upper region is an unsafe-speed zone where d > 55t. a.) The coordinate (3, 165) lies on the line d = 55t. What does the number 165 mean? b.) At what speed would a car be traveling to satisfy coordinates A(3, 275)? Is

this speed safe according to this graph? c.) At what speed would a car be traveling to satisfy coordinates B(5, 220)? Is this speed safe according to this graph?

Answer

3.

a.) What inequality is depicted by this see-saw? b.) Solve the inequality for x?

Answer

4.

Herman decides to take up golf. His golf club membership will cost $450 for the season and he will be charged $18 for each round of golf that he plays. Herman has decided not to spend more than $1000 on golf for the season. a.) Write an inequality that describes the relationship between the maximum amount Herman wants to spend and the total golf costs for the season. b.) Solve the inequality to determine the maximum number of rounds of golf he can play yet not exceed his $1000 limit.

Answer

5.Pizza Palace is running a promotional sale on cinnamon sticks. The hope is to attract more customers into the shop who will also buy a pizza with two toppings at the regular price. The Pizza Palace will lose $0.78 on very cinnamon stick order. The profit, however, on each pizza will be $1.32.

a.) "Breaking even" is the worst the Pizza Palace is willing to accept. They want the losses from the cinnamon sticks to be less than or equal to the profits from the pizzas. Write an inequality expression for this situation. Let c represent the number of cinnamon stick orders sold and p the number of pizzas. b.) Graph the inequality plotting the number of cinnamon stick orders on the horizontal axis and the number of pizzas on the vertical axis. Indicate the region where the Pizza Palace will profit from the promotion.

Answer

6.

An electronics store sells DVD players and cordless telephones. The store makes a $75 profit on the sale of each DVD player (d) and a $30 profit on the sale of each cordless telephone (c). The store wants to make a profit of at least $255 from its sales of DVD player and cordless telephones. Which inequality describes this situation?

Choose:Top of Form

75d + 30c < 255 75d + 30c < 255 75d + 30c > 255 75d + 30c > 255Bottom of Form

7.

A prom ticket at Smith High School is $120. Tom is going to save money for the ticket by walking his neighbor's dog for $15 per week. Tom has already saved $22. Which equation can be used to find the minimum number of weeks Tom must walk the dog to earn enough to pay for the prom ticket?

Choose:Top of Form

15x - 22 > 120 15x + 22 > 120 15x > 120 + 22 15x > 120Bottom of Form

1.

Player's HeightsKing is 76.5 inches tall. Boomer is 79 inches tall. Julie is 74.5 inches tall. Carmello is 77 inches tall. Timmy is 72 inches tall. Larry is 75.25 inches tall.

a.) 165 means that 165 miles are traveled. Since it takes 3 hours to cover the 165 miles, the speed is 165/3 or 55 mph. b.) A(2, 275) represents a distance of 275 miles covered in 2 hours at a speed of 275/2 or 91.7 mph. Unsafe zone. c.) B(5, 220) represents a distance of 220 miles covered in 5 hours at a speed of 220/5 or 44 mph. Safe zone.

3.

a.) The see-saw depicts x + 3 < 7. b.) x + 3 < 7 x 0.591c

4.

b.) The shaded region above the line identifies where the profits will be greater than the losses.

1.

In the set of positive integers, what is the solution set of the inequality 2x - 3 < 5 ?Top of Form

{0, 1, 2, 3} {1, 2, 3} {0, 1, 2, 3, 4} {1, 2, 3, 4}Bottom of Form

Answer

2.

Which of the following is not a solution of -4 < -6x + 2 < 8 ?Top of Form

0 1 2 -1Bottom of Form

Answer

3.

Which of the following expressions is represented by the graph shown below?Top of Form

Bottom of Form

4.

Ashley has a $20 bill and needs to buy three Hallmark Blossom birthday cards at $2.55 each. With the left over money she would like to buy as many Paw Note thank you cards as possible. If the thank you cards cost $2.99 each, how many thank you cards can she purchase? An algebraic solution is expected.Top of Form

3 thank you cards 4 thank you cards 5 thank you cardsBottom of Form

Answer

5.

Which expression has the entire number line as its graph? Choose:Top of Form

Bottom of Form

6.

Your new cell phone plan has a monthly access fee of $28.72 with a flat rate of $0.31 per minute. If you want to keep your monthly bill under $40, how many minutes per month can you talk on your new cell phone?

Answer 1.Solve the inequality: 2x - 3 < 5 2x < 8

x