Day 2: Solving One and Two Step Inequalities



Day 1: Writing and Graphing Inequalities

I. The Basic Symbols:

[pic] ______________________________________________

[pic] ______________________________________________

[pic] ______________________________________________

[pic] ______________________________________________

At Least ______________________________________________________

At Most ________________________________________________________

II. How to read a Number Line

Examples: For the following number lines, write the solution set as an inequality

1)

-3 -2 -1 0 1 2 3 4 5 6 7 8

2)

-5 -4 -3 -2 -1 0 1 2 3 4 5 6

3)

0 1 2 3 4 5 6 7 8 9 10 11

4)

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4

5)

4 5 6 7 8 9 10 11 12 13 14 15

When is the endpoint an open circle? A closed circle?

When does the arrow go to the right of endpoint? To the left of endpoint?

III. Graphing the solution set

Examples: For the following inequalities:

(a) graph the solution set

(b) Tell whether or not the given number is a member of the solution

1.) (a) n [pic] 8

(b) 8

2.) (a) n [pic] -6

(b) -20

3.) (a) 10.5 [pic] n

(b) 10.75

4.) (a) [pic]

(b) .8

5.) (a) [pic]

(b) -1.1

IV. Inequalities in Reverse form:

Identify numbers that fit the inequality described and sketch the graph. Rewrite with variable on the left-hand side of the inequality.

15 > x -9 ≤ x 0 < n 24 ≥ y

Day 2: Solving Using Addition & Subtraction

The sum of a number and seven is at most twenty-two. Write and solve an inequality for this situation.

Note: Solving one-step inequalities involving addition and subtraction is _____________ as solving one-step equations with these operations.

Ex Represent each of the following as an algebraic inequality. Solve and graph.

1) x plus five is at most 30 ___________________

2) 5 less than a number y is under 20 ___________________

Ex Solve each inequality and graph its solution set.

3) x – (-5) > 17 4) n + 5 < 24

5) 29 < x – 6 6) x + (-20) ≥ 12

7) x + 41 ≤ 26 8) x – (-19) > -8

Day 3: Solving Using Multiplication & Division

What makes solving an inequality different from solving an equation?

Ex Represent each of the following as an algebraic inequality. Solve and graph.

1) the sum of 5x and 2x is at least 14 ___________________

2) the product of x and six is less than or equal to 24 ___________________

Ex Solve each inequality and graph its solution set.

3) 5x > 30 4) -2n < 24

5) -39 > 3x 6) -4y) > -116

7) -15y ≥105 8) (1/2)m ≤ -17

Day 4: Solving Multi-Step Inequalities

Remember the steps for solving equations:

What makes solving Inequalities different?

Examples: Solve the following inequalities and graph their solutions

1.) 3x – 4 [pic] 17 2.) -2x + 5 [pic] 13

3.) 5 – 3x [pic] 14 4.) 2(2x – 8) – 8x [pic] 0

5.) -11 ≤ 6c + 1 6) 3(x – 1) – 2(1 – x) < 40

Day 5: Solving Inequalities with Variables on Both Sides

Recall: When variables are on both sides of the inequality symbol,

________________________________________________________________

Solve each inequality. Graph the solutions on a number line.

1. [pic] 2. [pic]

3. [pic] 4. 3a + (2a – 5) [pic] 13 – 2(a + 2)

Day 6: Inequality Word Problems

Identify some word phrases that indicate each inequality symbol.

|≤ |< |≥ |> |

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

How are these phrases different from the addition or subtraction operations?

Define a variable, write and inequality, and solve each problem.

1. Eight less than a number is no more than 14 and no less than 5.

2. The product of -5 and an number is greater than 35 or less than 10.

3. The length of a rectangle is 5 more than its width. The perimeter of the rectangle is at least 66. Find the minimum measure of the length and width.

4. Ms. Carter expects to pay 3 times as much for a jacket as for a blouse. If she has at most $100 to spend for both, what is the greatest amount she can spend on a blouse?

5. The greater of 2 integers is 8 more than three times the smaller. Their sum is greater than 28. Find the smallest possible values of the numbers.

6. Mrs. Scott decided that she would spend no more than $120 to buy a

jacket and a skirt. If the price of the jacket was $20 more than 3 times the price of the skirt, find the highest possible price of the skirt.

7. One positive integer is four times another, and their sum is at most 18. Find the largest possible values for the two numbers.

8. Joan needed $14 to buy some records. Her father agreed to pay her $3 an hour for gardening in addition to her $2 weekly allowance for helping around the house. What is the minimum number of hours Joan must work at gardening to earn $14 this week?

9. A salesperson earns $900 per month plus a commission of 3% of sales. How much must the salesperson well to have monthly income of at least $2,400?

10. Erika plans to take an 8-day trip. She wants to spend less than $1,200. If a motel room cost $60 each night, write and solve an inequality to find m, the amount she can spend each day for gas food and other expenses.

Day 7: Solving Compound Inequalities

What makes a compound inequality?

Graph the following inequalities:

1. [pic] 2. [pic]

3. [pic] 4. [pic]

5. [pic] or [pic] 6. [pic] or [pic]

Write a compound inequality for each graph.

1.

2.

[pic]

3. The cost of a new pair of sneakers ranges from $79 in one store to $120 in another. Write the inequality to represent the range of prices of the sneakers.

4. Each type of fish thrives in a specific range of temperatures. The optimum temperatures for sharks range form [pic]C to [pic]C, inclusive. Write an inequality to represent temperatures where sharks will not thrive.

Solve the following inequalities and graph the solution set.

TYPE I: And statements

1. [pic] Steps

2. [pic] 3. [pic] and [pic]

4. [pic] 5. [pic]

6. [pic] 7. [pic]

TYPE II: Or Statements

3. [pic] or [pic] Steps

4. [pic][pic] or [pic] 5. [pic] or [pic]

Mixed practice:

1. [pic] or [pic] 2. [pic]

3. [pic]or [pic] 4. [pic] and [pic]

-----------------------

4

3

-3

2

1

0

-1

-2

-5

-3

-4

-2

0

-1

2

1

................
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