Foundations of Math 2020 – 2021

Unit 6 Solving and

Graphing Inequalities

Name: ______________________________________

Teacher: ___________________________________

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Review!

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Inequality Symbols Graphing Inequality Symbols

> Greater Than The open circle indicates that this is NOT EQUAL TO the number graphed.

≥ Greater Than OR Equal To

(The line underneath the > means also equal to)

The closed circle indicates that this is EQUAL TO the number graphed.

< Less Than The open circle indicates that this is NOT EQUAL TO the number graphed.

≤ Less Than OR Equal To

(The line underneath the > means also equal to) The closed circle indicates that this is EQUAL TO the number graphed.

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Graphing Practice

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Name: ____________________________________________________ Date: _________________________ Lesson 6-1 A-REI.3

Examples:

The sum of x and 3 is less than 8.

5 subtracted from m is more than -11.

One half of a number is less than or equal to 3.

Three times a number is greater than or equal to negative nine.

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Practice: Solve each inequality and graph it on the number line.

1. 𝑥𝑥 + 17 ≥ 26 2. 𝑥𝑥 − 4 < 3 3. −8 + 𝑥𝑥 ≤ 5

4. 4𝑥𝑥 > 84 5. 13𝑥𝑥 ≥ −6 6. 𝑥𝑥

4< 2

7. A number divided by 8 is less than or equal to -5.

8. 84 is more than 4 times a number.

9. A number divided by 4 is at least -2.

ATTENTION: Special Rule for Inequalities!

When ______________________________________ or ____________________________________ both sides of an inequality by a

NEGATIVE NUMBER, the inequality symbol must be ___________________________________.

Example A: 𝑥𝑥−3

< 5 Example B: −5𝑥𝑥 ≥ 10

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TWO Name: ____________________________________________________ Date: _________________________ Lesson 6-2 A-REI.3

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Name: ____________________________________________________ Date: _________________________ Lesson 6-3 A-REI.3

Solving inequalities follow the same steps as solving equations! *Except that one SPECIAL RULE for multiplying or dividing by negatives (remember- this means to _____________ your inequality!).

Step 1) Get rid of parentheses by DISTRIBUTING! (___________________________ all terms inside by outside).

Step 2) On each side of the problem separately, COMBINE LIKE TERMS.

Step 3) Move all variable terms to the same side of the problem by adding or subtracting (use inverse!).

Step 4) Cancel out any constant hanging around the variable by adding or subtracting (use inverse!).

Step 5) Multiply or divide to eliminate the coefficient. This should leave you with an isolated variable!

(Don’t forget- flip your inequality symbol if multiplying or dividing both sides by a negative!)

Practice: Solve and graph the multi-step inequalities below. Show all work! 1. 4(𝑥𝑥 + 3) > −24 2. 𝑥𝑥 − 3(𝑥𝑥 + 2) ≥ 4

3. 6𝑥𝑥 + 1 < 9 − 2𝑥𝑥 4. 3 − (2𝑥𝑥 − 7) ≤ 34 − 6𝑥𝑥

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Practice with Multi-Step Inequalities!

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Name: ____________________________________________________ Date: _________________________ Lesson 6-4 A-REI.3, A-CED.1, A-CED.2

INEQUALITY WORD PROBLEMS Look for operation key words to help translate word problems into algebraic inequalities!

Remember the special phrases for inequalities!

DO NOW: Write down at least two-three phrases or key words that represent each inequality symbol. Refer back to page 5 if you need a refresher!

1. Nathan has lost his mother’s favorite necklace, so he will rent a metal detector to try to find it. A rental

company charges a one-time rental fee of $15 plus $2 per hour to rent a metal detector, Nathan has only $35 to spend. What is the maximum number of hours he can use the metal detector?

2. Connor wants to attend the carnival at Bald Hill this year. The price of admission to the fair is $4.50

and rides cost an additional $0.79 each. If he can spend at most $16.00 at the carnival, write an inequality and use it to find r, the number of rides Connor can go on.

< ≤

> ≥

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3. Keith has $500 in a savings account at the beginning of the summer. He wants to have at least $200 in

the account by the end of the summer. He withdraws $25 each week for food, clothes, and movie tickets. How many weeks can Keith withdraw money from his account? Justify your answer.

4. Yellow Cab Taxi charges $1.75 flat rate in addition to $0.65 per mile. Katie has no more than $10 to spend on a ride. Write an inequality that represents Katie’s situation and use it to determine how many miles Katie can travel in the cab without exceeding her budget. Show all work.

5. Janie has $3.00. She earns $1.20 for each chore she does. She wants to earn enough money to buy a CD

for $13.50. Write an inequality to determine the full number of chores, c, Janie could do to have enough money to buy the CD.

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Name: ____________________________________________________ Date: _________________________ Lesson 6-5 A-REI.10, A-REI.12

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Practice: Graph each linear inequality.

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Name: ____________________________________________________ Date: _________________________ Lesson 6-6 A-REI.6

1. 2.

3. 4.

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