Inequality Review

Chapter 2 Review Assignment

​Do you remember???

Multiple Choice

What is this symbol?

• less than

• greater than

• less than or equal to

• greater than or equal to

Multiple Choice

Which of these means that x is greater than or equal to 12

• x ≥ 12
• x  > 12
• x ≠ 12
• x ≥ 15

Multiple Choice

The sign below means... <

• Greater Than

• Less Than

• Greater Than or Equal to

• Less Than or Equal to

Multiple Choice

x is less than 9

• x < 9

• x > 9

• x ≥ 9

• x ≤ 9

Multiple Choice

Is the statement true or false?

-17 > -18

• True

• False

Multiple Choice

Is the statement true or false. -6 > -5

• True

• False

Multiple Choice

Write an inequality for this situation:  The restaurant can seat at most 172 people.

• x ≥ 172

• x ≤ 172

• x < 172

• x > 172

Multiple Choice

True or false less than is a closed dot?

$$<$$  

• True

• False

Multiple Choice

True or false greater than on a graph the arrow goes to the left?

• True

• False

Multiple Select

When does the inequality sign change?

• When adding

• When multiplying

• When dividing by a negative

• When multiplying by a negative

• When subtracting

Multiple Choice

Solve the following inequality:

x + 2 > 12

• subtract 2 from both sides and your answer is

  x = 10

• subtract 2 from both sides and your answer is

  x > 10

• subtract 2 from both sides and your answer is

  X < 10

Multiple Choice

Solve 5x > 10

• divide by 5 on both sides and your answer is

  x = 2

• divide by 5 on both sides and your answer is

  x < 2

• divide by 5 on both sides and your answer is

  x > 2

Multiple Choice

Solve 3x + 2 > 8

• subtract 2 from both sides and your answer is

  x > 6

• subtract 2 from both sides and your answer is

  x = 6

• subtract 2 from both sides and then divide by 3 on both sides and your answer is

  x > 2

Multiple Choice

Try some:

-2x ≤ 4

• divide by -2 o both sided and your answer will be

  x = -2

• divide by -2 on both sides and you will switch the direction of the inequality since you are dividing by a negative and your answer will be

  x ≥ -2

• divide by -2 on both sides and your answer will be

  x ≤ -2

Multiple Choice

- 3x < -12

• divide both sides by -3 and your answer is

  x < 4

• x = 4

• divide both sides by -3 and your answer is

  x > 4

  because you divided by a negative and had to flip the inequality symbol

Multiple Choice

Translate the following phrase:  Jessica must be at least 48 inches to ride the roller coaster.

• j > 48
• j < 48
• j ≤ 48
• j ≥ 48

Multiple Choice

Translate the following phrase: Edith must read for a minimum of 20 minutes every night.

• e > 20
• e < 20
• e ≥ 20
• e ≤ 20

Multiple Choice

Translate the following phrase: Grace has $45 at most in her purse on a daily basis

• g < 45
• g > 45
• g ≤ 45
• g ≥ 45

< Less Than

< Less Than or Equal To

Less than means go to the left on the Number line

> Greater Than

> Greater Than or Equal to

Greater than means go to the right on the Number Line

< or > = Open Circle

< or > = Closed Circle

Multiple Choice

Would x < 7 be a open or closed circle?

• open

• closed

Multiple Choice

Would x < -10 be a open or closed circle?

• open

• closed

Match

Match each statement with the correct graph.

y < 6

y > 6

y ≤ 6

y ≥ 6

• y < 6

• y > 6

• y ≤ 6

• y ≥ 6

Multiple Choice

What inequality does the number line graph represent?

• x ≤ 4

• x ≥ -4

• x < -4

• x < 4

Multiple Choice

What inequality does the number line graph represent?

• x >= 3
• x > 3
• x < -3
• x <= 3

Multiple Choice

Pick the correct letter for:

x < 6

• A

• B

• C

• D

Multiple Choice

What does an open circle mean?

• The number is opened.

• The number is part of the solution.

• The number is NOT part of the solution.

• It's just a shape, all points are equidistant from the center of the circle.

Multiple Choice

What does a closed circle mean?

• It means it is dark.

• The number is part of the solution.

• The number is NOT part of the solution.

• It's just a circle, all points are equidistant from the center of the circle.

Match

Match the inequality statement with its symbol.

• $$>$$  

• $$\le$$  

• $$\ge$$  

• $$<$$   

greater than

no more than

at least

less than

• greater than

• no more than

• at least

• less than

• You can buy either the $20 shirt or the $20 pullover.

• You can buy both the $20 shirt and the $20 pullover.

​

Which scenario is true?

​Situation 2 - You’ve earned $20 working.

• You can go to the birthday party or go to the ballgame.

• You can go to the birthday party and go to the ball game.

​

Are they the same thing?

Situation 1 - You parents tell you:

Discuss the difference in AND and OR in multiple situations:

• ​Formed by joining two statements with the word “OR.”

• Not alway common...apart...all possibilities...may not be true for all.​

​​Disjunction

​

• Formed by joining two statements with the word “AND.”

• Common...shared...together​

​​Conjunction

Definition

A compound inequality is made up of two inequalities connected by the word “AND” or the word “OR.”

WHat Do They look Like?

Pay attention to which one is the closed circle and which is the
open circle. If we interpret this graph, it means the solution(s)
to our inequality are less than or equal to -2 OR greater than 3.

How do I solve an “or” compound inequality?

Solve each inequality like you would a regular
inequality. However, when you graph on a number
line, you will have two graphed lines instead of
one.

We divided by a negative, so remember to flip the sign.
Because we flipped the sign, now flip around the
inequalities to read from left to right on a number line.

The other Type of Inequality…

Notice that the smaller value comes first (-6) and then the
larger value (1).

This is read as “x is
greater than or equal
to -6 AND less than or
equal to 1”

When reading these types
of compound inequalities,
start at the middle, then
the left, then the right.

WHat Do They look Like?

If you draw two lines under each inequality symbol, use this
as your balancing of each side. What you do to one of the
sides, you must do to ALL three sides.

How do I solve An “AND” compound inequality?

In order to get “x” by itself (isolate), I needed to

subtract 4. Notice how I subtracted 4 from BOTH sides of the

inequality.

Multiple Choice

Which graph represents  $$x\le-4$$  or  $$x>0$$  ?

Multiple Choice

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

Multiple Choice

Which graph matches the following "And" Compound Inequality

$$x>-2\ and\ x<3$$  

Multiple Choice

Write an inequality the graph

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

Multiple Choice

0 < x + 7 < 9

• -7<x   and   x<2
• -7<x   or   x<2
• -7>x   and   x>2
• -7>x  or   x>2

Multiple Choice

x + 8 < 3 or - 8x < -40 

• x > -5 or x < 5
• x < -5 and x > 5
• x < -5 or x > 5 
• x > -5 and x < 5 

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

-2 < x - 9 < 3

• x < 12

• 7 < x

• 7 < x < 12

Multiple Choice

Give the solution set for: -13<2x+5<15

• -9>x>5

• -9<x<5

• -4<x<5

• -4>x>5

Multiple Choice

$$-2<3y-4<14$$  How can you split up this inequality into two inequalities?

• $$-2<3y-4$$ and $$3y-4<14$$  

• You can't!

Multiple Choice

What word or phrase best describes the graph of an AND inequality?

• separate

• between

• not between

• annoying

Multiple Choice

What word or phrase best describes the graph of an OR inequality?

• inside

• between

• not between

• beautiful

Multiple Choice

When graphing "AND" inequalites, shading looks like___

• Shading that always connects the 2 dots.
• Shading that always points away from each dot
• 2 shaded arrows pointing in same direction(both left)
• 2 shaded arrows pointing in same direction (both right)

Multiple Choice

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

• Shading that connects the 2 dots
• Shading that points away and never crosses.
• Shading that points toward each other and ALWAYS crosses
• Shading that points opposite, but sometimes crosses.

Multiple Choice

-2x + 1 < 9 or x - 4 < 6

• x > 4 or x < 10

• -4 < x < 10

• x < -4 or x < 10

• All Real Numbers

Multiple Choice

Solve the following Compound Inequality $$-3<2x+3\le15$$  

• $$x>-3\ and\ x\ge6$$  

• $$-3>x\le6$$  

• $$x<-3\ and\ x<6$$  

• $$x>-3\ and\ x\le6$$  

Multiple Choice

Solve the following Compound Inequality $$2x+9>17\ or\ 5x+10<10$$  

• $$x<0\ or\ x<4$$  

• $$x>0\ or\ x>4$$  

• $$x<0\ or\ x>4$$  

• $$x>0\ or\ x<4$$  

Solving Inequality Steps

• Get rid of all Parentheses

• Combine like terms

• Move all x terms to the left hand side (LHS)

• Move all constants to the right hand side (RHS)

• Get rid of the x’s coefficient by doing the opposite operations (multiplication -> division or division -> multiplication)

• BE CAREFUL WHEN DIVIDING/MULTIPLYING BY A NEGATIVE

When you multiply or divide both sides by a negative, you FLIP the inequality sign!

​Some text here about the topic of discussion.

​SPECIAL RULE

Showing solutions

Poll

How do you feel about solving inequalities?

• Great!

• So-So.

• Confused?