Unit 2 Test Review- Solving Inequalities

Unit 2 Test Review

​Solving Inequalities

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​FOR CREDIT

​SHOW WORK FOR ALL 21 QUESTIONS

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​Inequality Rules!!

​1. If you multiply or divide by a negative on both sides, FLIP the Inequality sign!

​Inequality Rules!!

​2. Always write the variable(x) on the LEFT side!

NO! ​3<x

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​YES! x>3

Steps to solve a inequality:

​1. Distribute

​2. Combine like terms

​3. Move Variable to the LEFT SIDE

​4. Undo Addition and Subtraction First

​5. Flip the inequality if you multiply or divide by a negative.

​6. Make sure variable is on the left side. If not, reverse your answer.

Match

Match the following

• $$<$$

• $$>$$

• $$\le$$

• $$\ge$$

Less Than

Greater Than

Less Than OR Equal To

Greater Than OR Equal To

• Less Than

• Greater Than

• Less Than OR Equal To

• Greater Than OR Equal To

Multiple Choice

When graphing an inequality, you use an open dot when you use which symbol?

• <, >
• ≤, ≥ 
• ≤, <
• ≥, >

Multiple Choice

When graphing an inequality, you use an closed dot when you use which symbol?

• <, >
• ≤, ≥ 
• ≤, <
• ≥, >

Multiple Select

Which TWO inequalities match the graph? Choose the one with the variable on the LEFT and then reverse it.

• 11  $$\le$$  a

• 11  $$\ge$$   a 

• a  $$\le$$   11

• a  $$\ge$$   11

Multiple Choice

Do I need to flip my inequality when I solve this?
-3x  ≥ 12

• Yes, because I'll be dividing both sides by a negative 3 

• No, not this time.

Multiple Choice

Solve

(Hint: make sure you subtract 2 first, don't forget the flip rule)

• x < -20

• x > -20

• x > 20

• x < 20

Multiple Select

Solve.

-3x + 2 < -22

• x < 8

• x > 8

• x > 20/3

• x > 8

Hotspot

Solve and then select all the values in the solution set:

$$2\left(2b-3\right)>2\left(b-2\right)-6$$

Multiple Choice

Write the sentence as an inequality:

My sister plans to sell more than 250 boxes of cookies.

• c>250
• c<250
• c≤250
• c≥250

​Special Cases When The variable ELIMINATES

​NO SOLUTIONS if the inequality is FALSE

​6x + 5 > 6x +20

5 > 20​

is false so NO SOLUTIONS

​

​INFINTE SOLUTIONS if the inequality is TRUE

​6x -3 > 6x -10

​-3 > -10

​is true so ALL REAL NUMBERS

Multiple Choice

$$2x-3>2x+9$$  

• All Real Numbers

• no solution

Multiple Choice

$$6x+4<6x+10$$  

Solve

• all real numbers

• no solution

Compound Inequalities

Two Inequalities (or more) joined together with "AND" or "OR"

"OR" Compound Inequalities

On "OR" inequalities the graphs always go apart.

Solving "AND" Compound Inequalities

Remember, whatever you do do on the right must also be done on the left.

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​You are trying to get x alone in the middle.

"AND" Compound Inequalities

On "AND" inequalities the graphs always go together.

Multiple Choice

Solve and graph on your paper:  -3 ≤ 2x - 1 ≤ 5

• -1 ≤ x ≤ 3
• -1 < x < 3
• 1 < x < 3
• 1 ≤ x ≤ 3

Multiple Choice

Solve and graph

3x + 2 < -7 or -4x + 5 < 1

• All real numbers

• x < -3 and x > 1

• x < -3 or x < 1

• x < -3 or x > 1

Multiple Choice

When graphing the solutions to "OR" inequalities, The shading looks like___

• Shading that connects the 2 dots
• Shading in Opposite directions.

• Shading that points toward each other and ALWAYS crosses

Multiple Choice

When graphing "AND" inequalites, shading looks like___

• Shading that always connects the 2 dots.
• Shading that always points away from each dot
• Both shaded to the right

• Both shaded to the left

Multiple Choice

Which graph represents the compound inequality  $$-5<x<15$$  ?

Multiple Choice

Write an inequality for Graph 3.

• x ≤ -2 AND x > 5
• x ≤ -2 OR x > 5
• x ≥ -2 OR x < 5
• -2 ≤ x < 5

Multiple Choice

Emilia needs at least $240 to buy new headphones. She has already saved $30. She earns $14 per car that she washes.

What is the least number of cars she can wash to buy the headphones?

Define the variable.

• let x = Emilia

• let x = the number of cars she needs to wash

• let x = the number of headphones she wants to buy

• let x = the money she already saved

Multiple Choice

Emilia needs at least $240 to buy new headphones. She has already saved $30. She earns $14 per car that she washes.

What is the least number of cars she can wash to buy the headphones?

Write the inequality to the problem.

• 14x+30 ≥ 240

• 14x+30 ≤ 240

• 30x+14 ≥ 240

• 30x+14 ≤ 240

Multiple Choice

Emilia needs at least $240 to buy new headphones. She has already saved $30. She earns $14 per car that she washes.

What is the least number of cars she can wash to buy the

headphones?

Solve the inequality/answer the question.

• x ≥ 15

• x ≤ 15

• x > 15

• x < 15

Multiple Choice

You take a trip to the bowling alley, where each game cost $2, plus you plan to spend $10 on food. You can spend at most $25. Which inequality models this scenario?

• 2x + 10 ≥ 25

• 2x + 10 > 20

• 2x + 10 ≤ 25

• 2x + 10 < 25