Inequalities-8th Grade-TCAP

​Lesson: Inequalities

Let's Review

What are inequalities?

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 Select

Which set (s) of numbers make the inequality a - 5 < 6

• { 8,9,10}

• {11,12,13}

• {5,6,7}

Multiple Choice

No More Than

• <
• >
• ≤
• ≥

Multiple Choice

Fewer Than

• <
• >
• ≤
• ≥

Multiple Choice

more than

• <
• >
• ≤
• ≥

Graphing Inequalities

Match

Match the following inequality symbols:

• ≥

• ≤

• <

• >

Greater than or equal to

Less than or equal to

Less than

Greater than

• Greater than or equal to

• Less than or equal to

• Less than

• Greater than

Multiple Choice

x is greater than -7

• x < -7

• x ≤ -7

• x > -7

• x ≥ -7

Multiple Choice

x is greater than or equal to -7

• x < -7

• x ≤ -7

• x > -7

• x ≥ -7

Multiple Choice

Pick the correct graph for:
x ≥ 6

• A
• B
• C
• D

Multiple Choice

Write an inequality for the sentence:

The capacity of the theater is 437 people.

• $$p\ge437$$

• $$p\le437$$

• $$p>437$$

• $$p<437$$

Multiple Select

Which of the following are solutions of the inequality:

x ≥ 7

• 7

• -4

• $$\frac{1}{2}$$

• 10.6

• $$7\frac{2}{3}$$

Multiple Select

Which symbols below would be graphed with a filled in dot at the number?

Select all that apply.

• <

• ≥ 

• ≤

• >

• ΨΞ

Multiple Choice

What inequality does the number line graph represent?

• x > 5
• x < −5
• x ≥ 5
• x ≥ −5

Multiple Choice

Select the correct graph to represent the inequality $$s<20$$  

Multiple Choice

What inequality does the number line graph represent?

• b > –2
• b < –2
• b ≥ –2
• b ≤ –2

​If you multiply or divide both sides by a negative number, you must flip the inequality symbol.

Solve like an equation by isolating the variable on one side of the inequality.

​Solve Inequalities

-2x + 3 > 9

​-2x > 6

x < -3​

Multiple Choice

Solve.

$$3n+3\ge30$$  

• $$n\le9$$  

• $$n\ge9$$  

• $$n\le11$$  

• $$n\ge11$$  

Multiple Choice

Solve.

$$-8x+7<15$$  

• $$x>1$$  

• $$x<1$$  

• $$x>-1$$  

• $$x<-1$$  

Multiple Choice

Solve.

$$17\le-2m-3$$  

• $$-10\ge m$$  

• $$-10\le m$$  

• $$-7\ge m$$  

• $$-7\le m$$  

Multiple Choice

Solve.

$$17\le-2m-3$$  

• $$-10\ge m$$  

• $$-10\le m$$  

• $$-7\ge m$$  

• $$-7\le m$$  

Multiple Choice

$$Solve:\ 5\left(2+2x\right)>90$$  

• $$x<8$$  

• $$x<-36$$  

• $$x>8$$  

• $$x>-31$$  

Multiple Choice

$$Solve:\ -7\left(n-6\right)<91$$  

• $$n<7$$  

• $$n>7$$  

• $$n<-7$$  

• $$n>-7$$  

Linear Graph

An equation whose graph is a line is a linear equation. You can plot points on a coordinate plane to graph a linear equation.

Example: y = -4x + 4.

X and Y Intercepts

Linear equations have x and y-intercepts. The x-intercept is the x-coordinate of the point at which the graph crosses the x-axis. The y-intercept is the y-coordinate of the point at which the graph crosses the y-axis. 

Multiple Choice

What is the y-intercept?

• (0,15)

• (3,0)

• (15,0)

• (0,3)

Multiple Choice

What is the y-intercept?

• (2,0)

• (0,2)

• (0,-2)

• (-2,0)

Graphing Linear Inequalities

What are the solutions to a linear equality?

• Any point (x,y) that satisfies the inequality (makes it true)

• Any point (x,y) that is in the SHADED region when the inequality is graphed.

• Any point (x,y) that is ON THE LINE when the line is a SOLID LINE.

• Any points ON a dotted line are NOT solutions.

Dotted/Dashed Lines

• Dotted/Dashed Lines indicates not included

• Greater than shade above the line

• Less than shade below the line

Graphing Linear Inequalities is the same as graphing lines.

With the addition of shading above or below. We also have check if it is dotted or solid.

Multiple Choice

Is it shaded above or below?

$$y<-2x+3$$  

• above

• below

Multiple Choice

Is it shaded above or below?

$$y\ge\frac{1}{3}x-7$$  

• above

• below

Multiple Choice

Which is the correct graph?

• A

• B

• C

• D

Multiple Choice

Which is the correct graph?

• A

• B

• C

• D

Multiple Choice

Is it dotted or solid?  $y<\frac{1}{2}x+3$

 

• dotted

• solid

Multiple Choice

Is it dotted or solid?   $$y\ge3x-5$$  

• dotted

• solid

Multiple Choice

Which is the correct graph?

• A

• B

• C

• D

Multiple Choice

Which is the correct graph?

• A

• B

• C

• D

Multiple Select

Which point(s) are solutions to the inequality shown on the graph? Select all that apply.

• (-2,2)

• (0,3)

• (1,4)

• (-4,0)

• (5,-4)

Multiple Select

Which point(s) are solutions to the inequality shown on the graph? Select all that apply.

• (-2,1)

• (0,-2)

• (1,5)

• (3,-2)

• (5,2)

Multiple Choice

Which of the following equations match the given graph?

• y ≥ 2/5x + 1
• y ≥ -2/5x + 1
• y≤  2/5x + 1
• y ≥ -2/5x - 1

Multiple Select

Which point(s) are solutions to the inequality shown on the graph? Select all that apply.

• (0,5)

• (-2,2)

• (-3,4)

• (-1,1)

• (-4,0)

Multiple Select

Which point(s) are solutions to the inequality shown on the graph? Select all that apply.

• (-4,3)

• (1,3)

• (4,-5)

• (1,-5)

• (-3,-5)

Multiple Select

Which point(s) are solutions to the inequality shown on the graph? Select all that apply.

• (0,-4)

• (2,4)

• (-5,-1)

• (-4,-4)

• (1,-6)

Multiple Choice

Which graph best represents the following inequality?

Multiple Choice

Which of the following equations match the given graph?

• x ≥ -1
• x ≤ -1
• x > -1
• x < -1

Multiple Choice

Determine whether point (-3,-3) is a solution to the linear inequality that is shown.

• Yes

• No

• Sometimes

Multiple Choice

Choose the correct inequality for this graph.

Multiple Choice

Which of the following is the graph of

3x - 2y < 10

Systems of Inequalities

02/10/2021 - 02/11/2021

Graphing Systems of Linear Inequalities

~You will graph each linear inequality separate.

~The part where the shadings overlap is where you will find your solutions

~You can graph this by hand or use the calculator

Graphing linear inequalities by hand

Graphing using a calculator

Multiple Choice

Use desmos. Which correctly shows the graph of the sytem:

$$y<-\frac{3}{2}x+1$$  
$$x\ge-2$$  

Multiple Choice

Use desmos to pick the correct graph of the system:
$$y<x$$  
$$y\ge-\frac{1}{2}x+1$$  

Multiple Choice

The graph shows which system?

• 
  

  $$y>\frac{2}{3}x+1$$
  

  
  $$y\le-5x+10$$
  

• $$y<\frac{2}{3}x+1$$
  $$y\ge-5x+10$$
  

• $$y<\frac{2}{3}x+1$$
  $$y\le-5x+10$$
  

• $$y>\frac{2}{3}x+1$$
  $$y\ge-5x+10$$
  

Multiple Choice

Which point is a solution to both inequalities?

• (-10,-5)

• (-20,25)

• (40,30)

• (40,-10)

Multiple Select

Pick ALL correct answers.

Which are solutions to the system?

• (-5,4)

• (-5,-2)

• (0,10)

• (5,10)

• (0,-5)

Luka and Dana are making cookies for the Westland Pantry. They only have up to 6 hours to bake! They can bake 32 chocolate chip cookies in an hour (x), and 20 snickerdoodle cookies in an hour (y). They need to make at least 150 cookies. Which inequalities represent the situation?

Multiple Choice

Kate is selling bracelets and earrings on Etsy to make money for summer vacation. The bracelets (x) cost $2 and earrings (y) cost $3. She needs to make at least $100, but can only make up to 40 pieces of jewelry. Which inequalities represent this situation?

• 2x + 3y > 100

  x + y ≤ 40

• 100x + 2y > 3

  x + y ≤ 40

• 100x + 40y > 100

  3x + 2y ≤ 40

• 3x + 2y > 100

  x + y ≤ 40

Multiple Choice

Will this inequality have a solid or dashed boundary line?

$$y\ \le\ \frac{2}{3}x\ +\ 8$$  

• solid

• dashed

Multiple Choice

Which of the following equations match the given graph?

• y ≤ -5/4 x + 3

• y ≥ -5/4 x + 3

• y < -5/4 x + 3

• y > -5/4 x + 3

Multiple Choice

Will this inequality have a solid or dashed boundary line?

$$y\ \ge\ 2x\ -\ 3$$  

• solid

• dashed

How do you shade?

How do you know when it's a solid or dashed boundary line?

Multiple Choice

Which of the following has the shaded region less than the boundary line?

Multiple Choice

Which of the following has the shaded region less than the boundary line?

Multiple Choice

Identify the graph that has the shaded region above the boundary line?

Describe the inequality's boundary line and shaded region.

• solid line

• shade below

Multiple Choice

Which point below is NOT a part of the solution set?

• (0, 0)
• (0, 1)
• (-100, -3)
• (5, 10)

Multiple Choice

Which point below is NOT part of the solution set?

• (0, 0)
• (-10, -10)
• (-1, 5)
• (5, 20)

Multiple Choice

Which of the following equations match the given graph?

• y ≤ -3/4 x + 3
• y ≥ -3/4 x + 3
• y < -3/4 x + 3
• y > -3/4 x + 3