Unit 6 Equations and Inequalities

Equations Equations Equations!

One Step Equations

These are equations you can solve in one step by doing the OPPOSITE operation.

Multiple Choice

Solve x + 6 = 10

• 10

• 6

• 4

• 16

Multiple Choice

Solve x - 10 = 21

• 21

• 10

• 11

• 31

Multiple Choice

Solve 7x = 42

• 7

• 6

• 42

• 35

Multiple Choice

Solve

$$\frac{x}{4}=12$$  

• 4

• 3

• 12

• 48

Two Step Equations

• These are equations that you can solve in two steps

• Typically, the FIRST step is to take care of any addition or subtraction

• Typically, the SECOND step is to take care of any multiplication or division

• There are SOME cases where the steps may be different, but that is usually if you have exponents, parentheses, or a BIG division problem

Multiple Choice

Solve 7x - 5 = 30

• 25/7

• 5

• 35

• 245

Multiple Choice

Solve 8 + 4x = 24

• 2

• 4

• 8

• 24

Multiple Choice

Solve

$$\frac{x}{2}-11=13$$  

• 4

• 48

• 24

• 12

Multiple Choice

Solve (HINT - take care of the division FIRST, then the addition)

$$\frac{x+4}{7}=8$$  

• 52

• 60

• 28

• 84

Multi Step Equations

• DISTRIBUTE first

• COMBINE second

• Get x's on one side

• SADME to finish

Multiple Choice

Solve 2x + 3x - 6 = 14

• 20

• 10/3

• 4

• 14

Multiple Choice

Solve 4x - 2 = 2x + 16

• 9

• 18

• 2

• -9

Multiple Choice

Solve -4(3x - 6) = 48

• -6

• -2

• 2

• -12

Multiple Choice

Challenge Question: Solve 10 - (4x - 3) = 2x - 7

• 10/3

• 7/3

• 5/2

• 17

Inequalities

Understand solving an inequality as a process of answering a question: which values from a specified set, if any, inequality true? Use substitution to determine whether a given number in a specified set makes the inequality true.

Remember Inequality Symbols

Points to the Left - Less

Points to the Right - gReater

Multiple Choice

Draw a graph for x > 0

x > 0

x is gReater (point to the Right)

Multiple Choice

Draw a graph for x > 5

x > 5

x is gReater than 5 (points to the Right)

Multiple Choice

Write an inequality for the following graph

Inequality

Multiple Choice

What is this symbol?

• less than

• greater than

• less than or equal to

• greater than or equal to

Examples of Inequalities

Multiple Choice

What symbol could go in the box to make a true statement?
9 ___  -9

• >
• <
• ≥
• ≤

Multiple Choice

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

• x ≥ 12
• x  > 12
• x ≠ 12
• x ≥ 15

Steps to determine if a number is part of the solution set:

1. Read the inequality from the variable and put it in your own words

2. substitute the given number and evaluate

3. Decide if the number makes the inequality true.

Multiple Choice

No More Than

• <
• >
• ≤
• ≥

Multiple Choice

Fewer Than

• <
• >
• ≤
• ≥

Multiple Choice

more than

• <
• >
• ≤
• ≥

Multiple Choice

What inequality does the number line graph represent?

• x >= 3
• x > 3
• x < -3
• x <= 3

Multiple Choice

What inequality does the number line graph represent?

• x ≤ 4

• x ≥ -4

• x < -4

• x < 4

Multiple Choice

Which inequality matches the graph?

• x<3

• x>3

• x<3

• x>3

Multiple Choice

Which inequality matches the graph?

• x>-2

• x<-2

• x>-2

• x<-2

Multiple Select

Select all values that are solutions to the inequality x < 20

• 0

• 100

• 10

• 50

Multiple Choice

Less than or equal to

• <
• >
• ≤
• ≥

Multiple Choice

Greater than or equal to

• <
• >
• ≤
• ≥

Multiple Choice

Match the graph with its inequality.

• a > 11

• a < 11

• a ≥ 11

• a ≤ 11

Multiple Choice

Match the graph with its inequality.

• b > –2
• b < –2
• b ≥ –2
• b ≤ –2

Multiple Choice

Pick the correct letter for:

x < 6

• A

• B

• C

• D

Multiple Choice

Which inequality represents the graph?

• X < 4

• X undefined4

• X > 4

• X $$\ge$$ 4

Multiple Choice

Which inequality represents the graph?

• X > 3

• X $$\ge$$ 3

• X < 3

• X $$\le$$ 3

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

Two-step inequalities

• The symbol is less or equal

• Undo subtraction by adding 5 to both sides

• Undo multiplication by dividing by 3 on both sides

• Graph on the number line

• Circle is filled and arrow points to the left

Multiple Choice

Solve an inequality

Solve an inequality

• Symbol gReater or equal to (points to the Right)

• Undo subtraction by adding 3 to both sides

• Undo division by multiplying by 6 both sides

• Graph on the number line

• Circle is filled and arrow points to the right

Multiple Choice

What answer did you get for the previous question?

Solve and graph an inequality

• Distribute 4 to 8x and -6

• Undo subtraction by adding 24 to both sides

• Undo multiplication by dividing by 32 on both sides

• Graph on the number line

• Circle is filled and arrow points to the left

Multiple Choice

What answer did you get for the previous question?

Solve and graph an inequality

• Distribute 4 to 8a and -6

• Combine Like terms 32a and a

• Undo subtraction by adding 24 to both sides

• Undo multiplication by dividing by 33 on both sides

• Graph on the number line

• Circle is empty and arrow points to the Left (Less)

Multiple Choice

What answer did you get for the previous question?

Multiple Choice

$$3(x-2)<2(x+9)$$

• $$x<24$$

• $$x>12$$

• $$x<12$$

• $$x>24$$

Multiple Choice

$$-4\left(x-9\right)+2x\ge-27$$  

• $$x\le-31.5$$

• $$x\le31.5$$

• $$x\ge31.5$$

• $$x\ge-31.5$$

Multiple Choice

You flip an inequality symbol when you...

• subtract

• multiply and divide only

• multiple by a negative number

• multiple or divide by a negative number