Equations and Inequalities

Equations and Inequalities

By Courtney Tout

Multiple Choice

What is the goal of solving equations and inequalities?

• To get all the numbers on one side of the symbol

• To isolate the variable

• To use inverse operations to graph

• To make math difficult

Step 1: Use Inverse to Undo Constants

Step 2: Use Inverse to Undo Coefficient

Step 3: Plug in and Check​

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​Two Step Equations

Multiple Choice

3c + 5 = 23

• c = 3
• c = 6
• c = 7
• c = 18

Multiple Choice

What is the first step to solve this equation:
11 - 3x = 44

• Add 3 to both sides
• Subtract 11 from both sides
• Add 11 to both sides
• Divide 3 on both sides.

Multiple Choice

Level 3

Identify the steps to solve for b

• Add 6 to both sides and divide both sides by 5

• Add 6 to both sides and multiply both sides by 5

• Subtract 6 from both sides then multiply both sides by 5

• Subtract 6 from both sides then divide both sides by 5

Multiple Choice

$$5x-1=19$$  

• $$x=4$$  

• $$x=10$$  

• $$x=5$$  

• $$x=15$$  

Multiple Choice

$$\frac{x}{4}+8=10$$  

• $$x=-4$$  

• $$x=-8$$  

• $$x=8$$  

• $$x=16$$  

Multiple Choice

20 = 2 - a

• a= 18
• a= -18
• a= -10
• a= 12

Multiple Choice

The steps in solving 5b - 6 = 24 are: 

• Add 6 to both sides and divide both sides by 5
• Add 6 to both sides and multiply both sides by 5
• Subtract 6 from both sides then multiply both sides by 5
• Subtract 6 from both sides then divide both sides by 5

Multiple Choice

13= 5m -2

• -3

• 2

• 3

• -2

Multiple Choice

4x + 7 = 23

• x = 16
• x = 4
• x = 9
• x = 12

Multiple Choice

6p - 5 =13

• 12
• 15
• 3
• -3

Exact same process as Equations

​

Only Difference:

If you multiply or divide by negative number you must FLIP the Inequalitiy SYMBOL​

--> Negative Numbers in front of the variable do this.​

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Two Step Inequalities

Multiple Choice

Find the solution

• $$X\ge4$$

• $$X\le4$$

• $$X\ \le\ 10$$

• $$X\ >\ 4$$

Multiple Choice

Find the solution

• $$X\ \le\ 6.5$$

• $$X\ >2$$

• $$X\ \ge\ 10$$

• $$X\ \le\ 10$$

Multiple Choice

16 - 4a > 8

• a<-2
• a>-2
• a<2
• a>2

Multiple Choice

Do I need to flip my sign?
-3x  ≥ 12

• Yes
• No

Multiple Choice

Do I need to flip my sign?
3x  ≥ 12

• Yes
• No

​Graphing Inequalities

Multiple Choice

When you graph an inequality, you use a closed dot when you use which symbols?

• ≤, ≥

• <, >

Multiple Choice

When graphing an inequality, you use an open dot when you use which symbol?

• <, >
• ≤, ≥ 

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 the arrow point left or right?

• Left

• R

Multiple Choice

Match the graph with its inequality.

• b > –2
• b < –2
• b ≥ –2
• b ≤ –2

Multiple Choice

What inequality does the number line graph represent?

• x ≤ -4
• x ≥ -4
• x < -4
• x < 4

Multiple Choice

Match the graph with its inequality.

• a > 11
• a < 11
•  a  ≥ 11
•  a ≤ 11

Multiple Choice

Choose the correct graph that best describes the solution for each inequality
5 + x ≥ 29

• a
• b
• c
• d

Multiple Choice

Which number line shows the solution to:
11x + 14 < –8? 

• a
• b
• c
• d