Day 5 - Solving & Graph Linear Inequalities

Multiple Choice

Take the inequality 6 > 2.

Is this still true, if you

Add 3 to both sides.

• True

• False

Math Response

Take the inequality 6 > 2.

if you

Add 3 to both sides.

What is your new inequality? 

Type answer here

Correct Answer: 9>5

Deg^°

Rad

Multiple Choice

Take the inequality 6 > 2.

Is this still true, if you

Subtract 3 from both sides.

• True

• False

Math Response

Take the inequality 6 > 2.

if you

Subtract 3 from both sides.

What is your new inequality?

Type answer here

Correct Answer: 3>-1

Deg^°

Rad

Multiple Choice

Take the inequality 6 > 2.

Is this still true, if you

Multiply both sides by 3. What is your new inequality?

• True

• False

Math Response

Take the inequality 6 > 2.

if you

Multiply both sides by 3.

What is your new inequality?

Type answer here

Correct Answer: 18>6

Deg^°

Rad

Multiple Choice

Take the inequality 6 > 2.

Is this still true, if you

Multiply both sides by -3 and do not flip the sign.

• True

• False

Math Response

Take the inequality 6 > 2.

if you

Multiply both sides by -3.

What is your new inequality(do not flip the sign)?

Type answer here

Correct Answer: -18>-6

Deg^°

Rad

Multiple Choice

Take the inequality 6 > 2.

Is this still true, if you

Divide both sides by 2. What is your new inequality?

• True

• False

Math Response

Take the inequality 6 > 2.

if you

Divide both sides by 2.

What is your new inequality?

Type answer here

Correct Answer: 3>1

Deg^°

Rad

Multiple Choice

Take the inequality 6 > 2.

Is this still true, if you

Divide both sides by -2 and do not flip the sign.

• True

• False

Math Response

Take the inequality 6 > 2.

if you

Divide both sides by -2

What is your new inequality(do not flip the sign)?

Type answer here

Correct Answer: -3>-1

Deg^°

Rad

Multiple Choice

A solution to an inequality is any number that makes the inequality true. 

2x – 4 ≥ -12

x = -2

Is the inequality true?

• True

• False

Multiple Choice

A solution to an inequality is any number that makes the inequality true. 

2x – 4 ≥ -12

x = -4

Is the inequality true?

• True

• False

Multiple Choice

A solution to an inequality is any number that makes the inequality true. 

2x – 4 ≥ -12

x = -6

Is the inequality true?

• True

• False

Drag and Drop

When graphing inequalities:

Use an open circle for ​​

Placeholder

.

Use a closed circle for ​​​​

Placeholder

.

Drag these tiles and drop them in the correct blank above

> or <

≥ or ≤

Multiple Choice

When graphing b ≤ 6 would you use an open or closed circle?

• Open

• closed

Multiple Choice

When graphing b< 6 would you use an open or closed circle?

• Open

• closed

Multiple Choice

Which graph matches the inequality
k < 3?

• A

• B

• C

• D

Multiple Choice

Which inequality matches the graph?

• A

• B

• C

• D

Multiple Choice

Which inequality matches the graph?

• A

• B

• C

• D

Multiple Choice

Match the graph with its inequality.

• 11 < a

• 11 > a

•  11 ≤ a

•  11 ≥ a

Multiple Choice

Pick the correct inequality.

• A

• B

• C

• D

Multiple Choice

Pick the correct letter for:
6 > x

• A

• B

• C

• D

Multiple Choice

What are two solutions to x < 8?

• 8.6, 7.9

• 11, 16

• 0.8, 5.9

• 12, 7.1

Drag and Drop

x ≥ 7



x is ​

Placeholder

seven.

The graph will have a/an ​

Placeholder

circle at 7 and the arrow will be graphed going in the ​

Placeholder

direction.

Drag these tiles and drop them in the correct blank above

greater than or equal to

closed

positive

less than or equal to

greater than

not quite

no less than

much bigger

open

negative

Drag and Drop

x < 3



x is ​

Placeholder

three.

The graph will have a/an ​ ​

Placeholder

circle at 3 and the arrow will be graphed going in the ​

Placeholder

direction.

Drag these tiles and drop them in the correct blank above

fewer than

open

negative

greater than

no less than

much bigger

closed

positive

Draw

Graph "x is bigger than 5"

Draw

Graph x ≤ -3

Draw

Draw the graphs of each inequality

Multiple Choice

What inequality does the number line graph represent?

• x≥ 3

• x > 3

• x < -3

• x ≤ 3

Multiple Choice

Match the graph with its inequality.

• c > 9

• c < 9

• c ≥ 9

• c ≤ 9

Multiple Choice

Match the graph with its inequality.

• a > 11

• a < 11

• a ≥ 11

• a ≤ 11

Match

Match each statement with the correct graph.

y < 6

y > 6

y ≤ 6

y ≥ 6

• y < 6

• y > 6

• y ≤ 6

• y ≥ 6

Drag and Drop

When solving inequalities, if you multiply or​ ​

Placeholder

both sides by a ​

Placeholder

number, you must ​

Placeholder

the ​

Placeholder

symbol.

Drag these tiles and drop them in the correct blank above

divide

negative

reverse or flip

inequality

add

positive

equal

Multiple Choice

$$-8x+7<15$$  

Explain when we would reverse the inequality sign when solving this inequality.

•  When subtracting 7 from both sides.

•  When dividing both sides by 8.

•  When dividing by -8.

•  We would not reverse the sign because 15 is positive.

Drag and Drop

If 64 ≥ 8x

then 8x​​

Placeholder

64

and

x = ​

Placeholder

Drag these tiles and drop them in the correct blank above

≤

8

≥

<

>

-8

6

-6

12

-12

Multiple Choice

Describe the steps to solve the inequality:

$$3x-4>30$$  

•  Step 1: Subtract 30 from both sides.

  Step 2: Divide both sides by 3.

•  Step 1: Add 4 to both sides.

  Step 2: Divide both sides by 3.

•  Step 1: Divide both sides by 3. 

  Step 2: Add 4 to both sides.

•  Step 1: Add 4 to both sides.

  Step 2: Divide both sides by -3.

Match

Match the appropriate step to each equation.

• 180 = 8x - 20 + 2x

• 35 = 7x

• 15 = 3x - 6

• $$8\ =\ \frac{x}{42}$$

• 29 = 3x + 8

Combine like terms.

Divide both sides by _.

Add _ to both sides.

Multiply both sides by _.

Subtract both side by _.

• Combine like terms.

• Divide both sides by _.

• Add _ to both sides.

• Multiply both sides by _.

• Subtract both side by _.

Match

Match the appropriate step to solve each inequality.

• 150 > 5x - 20 + 4x

• 35 < 7x

• 15 ≥ 5x - 15

• $$8\ >\ \frac{x}{42}$$

• 49 ≤ 4x + 9

Combine like terms.

Divide both sides by _.

Add _ to both sides.

Multiply both sides by _.

Subtract both side by _.

• Combine like terms.

• Divide both sides by _.

• Add _ to both sides.

• Multiply both sides by _.

• Subtract both side by _.

Multiple Choice

Here is the inequality $$4\ <\ 3x\ +\ 2$$  is x = 0 a solution?

• Yes, the solution is less than 4

• Yes, the solution is greater than 4

• No, the solution is less than 4

• No, the solution is greater than 4

Multiple Choice

Solve the inequality 3x - 2 > 5x + 10

• -6 > x

• -6 < x

• 8 > x

• 8 < x

Multiple Choice

Which graph represents the inequality 2x + 3 < 7

Multiple Choice

Solve and graph the inequality.
77 ≤ 5 + 8n

• A

• B

• C

• D

Multiple Choice

• A)

• B)

• C)

• D)

Multiple Choice

Graph the solution set of the inequality.

–4n + 1 > –23

Multiple Choice

Graph the solution set of the inequality.

–4a ≤ –28

Match

Match the following

• means that the solutions is all numbers between 8 and 24 including 8 and 24.

• means that the solution is all numbers between 8 and 24 not including the numbers 8 and 24.

• means that the solution is all numbers between 8 and 24, including 8 but not including 24.

• means that the solution is all real numbers

• means that the solution is all numbers greater than 8, not including 8.

[ 8, 24 ]

(8, 24)

[8, 24)

(-∞, ∞)

(8, ∞)

• [ 8, 24 ]

• (8, 24)

• [8, 24)

• (-∞, ∞)

• (8, ∞)

Multiple Choice

Express the following in Interval Notation
-8 ≤ x < 8

• [-8, 8]

• [-8,8)

• (-8, 8]

• (-8, 8)

Multiple Choice

Express the following in Interval Notation
-9 < x ≤ -4

• [-9, -4]

• (-9,-4]

• [-9, -4]

• (-9,-4)

Multiple Choice

Express the following interval in Set notation:
[3, 5]

• 3 ≤ x ≤ 5

• 3 < x ≤ 5

• 3 ≤ x < 5

• 3 < x < 5

Multiple Choice

Express the following interval in Set notation:
(-7, 15]

• -7 ≤ x ≤ 15

• -7 < x ≤ 15

• -7 ≤ x < 15

• -7 < x < 15

Multiple Choice

What is the correct inequality notation for the graph shown?

• $$-2<x\le1$$  

• $$-2<x<1$$  

• $$-2\le x<1$$  

• $$-2\le x\le1$$  

Multiple Choice

$$x\le3$$  

is equivalent to which interval?

• $$\left(-\infty,\ 3\right)$$  

• $$\left(-\infty,\ 3\right]$$  

• $$\left(3,\ \infty\right)$$  

• $$\left[3,\ \infty\right)$$  

Multiple Choice

$$-2<x\le5$$   is equivalent to which interval?

• $$\left(-2,\ 5\right)$$  

• $$\left(-2,\ 5\right]$$  

• $$\left[-2,\ 5\right]$$  

• $$\left[-2,\ 5\right)$$  

Multiple Choice

$$\left(-3,\ 5\right)$$   is equivalent to which set notation statement?

• $$-3<x>5$$  

• $$-3\ge x\ge5$$  

• $$-3\le x\le5$$  

• $$-3<x<5$$  

Multiple Choice

$$\left(-\infty,5\right]$$   is equivalent to which set notation statement?

• $$x>5$$  

• $$x<5$$  

• $$x\le5$$  

• $$x\ge5$$  

Multiple Choice

Write the inequality in interval notation.

• [-4, -1)

• (-4, -1)

• (-4, -1]

• [-4, -1]

Multiple Choice

What interval notation does the number line graph represent?

• [∞, -5)

• (∞, -5)

• [-5, ∞)

• (-5, ∞)