Introduction to Inequalities

Introduction to Inequalities

Day 1

So far we have just used the equal symbol to determine if statments are true or false

• For example 2 + 4 = 6 is true

• And 2 + 4 = 5 is false

The Symbol   $>$   means "Greater Than"

For example,  $2\ +\ 5\ >\ 6$  

Multiple Choice

Which of these following statments are true?

• 4 + 9 > 19

• 4 + 9 > 13

• 4 + 9 > 5

The Symbol   $\ge$   means "Greater Than or equal to"

For example,  $2\ +\ 5\ \ge\ 7$  

Multiple Select

Select all of the following options that are true statements

• 2 + 4 $\ge$ 6

• 2 + 4 $\ge$ 7

• 2 + 4 $\ge$ 100

• 2 + 4 $\ge$ 1

The Symbol   $<$    means "Less Than"

For example,  $2\ +\ 5\ <\ 10$  

Multiple Choice

Which of these following statments are true?

• 4 + 9 < 20

• 4 + 9 < 9

• 4 + 9 < 13

The Symbol   $\le$   means "Less Than or equal to"

For example,  $2\ +\ 5\ \le\ 7$  

Multiple Select

Which of these following statments are true?

• 4 + 9  $\le$  20

• 4 + 9   $\le$  9

• 4 + 9   $\le$ 13

Multiple Choice

If I replace 𝑥 with 3, is 5 + 𝑥 = 8 a true statement?

• Yes

• No

Open Ended

Why was 5 + 𝑥 = 8 true when 𝑥 = 3?

Multiple Choice

Is 5 + 𝑥 > 8 a true statment if I replace 𝑥 with 3?

• Yes

• No

If I replace 𝑥 with 3, then 5 + 𝑥 > 8 becomes 5 + 3 > 8.

5 + 3 = 8, so The above statment is 8 > 8

Can 8 Be greater than 8? No, so the statment is false.

Multiple Choice

If I replace 𝑥 with 3, is 5𝑥 = 8 a true statement?

• Yes

• No

Multiple Choice

If I replace 𝑥 with 3, will 5𝑥 > 8 be a true statement?

• Yes

• No

If I replace 𝑥 with 3, then 5𝑥 > 8 becomes 5*3 > 8.

5 *3 = 15, so The above statment is 15 > 8

Is 15 greater than 8? Yes, so the statement is true.

Fill in the Blank

 $y+6=16$  

What value(s) does the variable have to represent for the equation or inequality to result in a true number sentence?

Type in just the number

Fill in the Blank

 $3g=15$  

What value(s) does the variable have to represent for the equation or inequality to result in a true number sentence?

Type in just the number

Fill in the Blank

 $3g<15$  for this inequality, the variable g could represent any number smaller than 5.

In  $3g\le15$  the variable could also represent any number smaller than 5, but it could also be one other number... What is that number?

Type in just the number

Open Ended

 $y+6>16$  

What value(s) does the variable have to represent for the equation or inequality to result in a true number sentence?

Multiple Select

 $m+4=12$  
Which of the following number(s), if any, make the equation or inequality true: 

• 0

• 3

• 5

• 8

• 10

Multiple Select

 $m+4<12$  
Which of the following number(s), if any, make the equation or inequality true: 

• 0

• 3

• 5

• 8

• 10

Multiple Select

 $\frac{1}{2}w=6$  

Choose the number(s), if any, that make the equation or inequality true from the following set of numbers:

• 2

• 4

• 6

• 12

• None of the options

Multiple Select

 $\frac{1}{2}w\le6$  

Choose the number(s), if any, that make the equation or inequality true from the following set of numbers:

• 2

• 4

• 6

• 12

• None of the options

Multiple Select

 $5h=40$  

Choose the number(s), if any, that make the equation or inequality true from the following set of numbers:

• 2

• 4

• 6

• 12

• None of the options

Open Ended

Consider the equation 𝑦 + 3 = 11 and the inequality 𝑦 + 3 < 11. How does the solution to the equation help you determine the solution set to the inequality?

When you submit your answer, please move on to the next step of the Do Now.