1. 9/18/2017 – Pop Quiz Question 1) 2x+4≥ 24 Solve for x Graph Question 2
8 < -5b -2
Step 1
Step 2
Question 3)
m > 2n + b
Solve for b

2. Translating Inequalities
Old Math Symbols
> Greater than
< Less than
New Math Symbols
Greater than or equal to
Less than or equal to

3. Identify Key Words
Read the mathematical problem and identify key terms or phrases that can be translated into an inequality symbol.

4. Greater than or equal to
Key Vocabulary
Phrase
Meaning
Mathematical Symbol
At most
No more than
Less than or equal to
At least
No greater than
Greater than or equal to

5. Examples Verbal Expression You can spend at most $20 Meaning
You can spend $20 or any amount less than $20
Math Expression
A person must be at least 18 to vote
A person who is 18 years old or any age older than 18 may vote

6. Additional Key Phrases
Symbol
Exceeds
Is more than
Is at least
Is at most

7. Practice Problems
More than 18,000 fans attended the Kings’ opening hockey game at the Staples Center in Los Angeles.
Your height is greater than 40 inches.
The sum of two numbers is at most 6.

8. Memory Strategy Vocabulary Word Translation At Most and no More than
Less than or equal to
At Least and no Less than
Greater than or equal to

9. Literal Equations
solve literal equations (formulas) for a specified variable.
Standard:
SOL: A.4a
A literal equation is an equation that contains more than one variable.
When solving a literal equation, you rearranging the equation to isolate the variable.

10. 1) Solve 2x - 4y = 7 for x To get x by itself, what is the first step?
Add 2x
Subtract 2x
Add 4y
Subtract 4y
Answer Now

11. 1) Solve 2x - 4y = 7 for x Use a DO-UNDO chart to help determine the steps
Ask yourself,
What is the first thing we are doing to x?
What is the second thing?
DO UNDO
· 2
-4y
Follow the steps in the ‘undo’ column to isolate the variable.
+4y
÷ 2
Complete the undo column by writing the opposite operations in opposite order.

12. 1) Solve 2x - 4y = 7 for x + 4y + 4y 2x = 7 + 4y 2 2 Draw “the river”
D U
· 2
-4y
+4y
÷ 2
+ 4y + 4y
2x = y
Draw “the river”
Add 4y to both sides
Simplify
Divide both sides by 2
Does it simplify?
This fraction cannot be simplified because both terms in the numerator are not divisible by 2.

13. 2) Solve 2x - 4y = 7 for y To get y by itself, what is the first step?
Add 2x
Subtract 2x
Add 4y
Subtract 4y
Answer Now

14. 2) Solve 2x - 4y = 7 for y - 2x - 2x -4y = 7 - 2x -4 -4
D U
· -4
+2x
-2x
÷ -4
- 2x x
-4y = 7 - 2x
Draw “the river”
Subtract 2x from both sides
Simplify
Divide both sides by -4
Does it simplify?
Nope!

15. 3) Solve for y. What is the first step?
Multiply by 3
Divide by 3
Add a
Subtract a
Answer Now

16. 3) Solve for y: y + a = 3c -a -a y = 3c - a Draw “the river”
D U
+ a
÷ 3
· 3
- a
Draw “the river”
Clear the fraction – multiply both sides by 3
Simplify
Subtract a from both sides
y + a = 3c
-a -a
y = 3c - a

17. 4) Solve for y: 4x – 2y = 12 -4x + 12 4x - 12 -2x + 6 2x - 6
Answer Now

18. 4) Solve for y: 4x – 2y = 12 - 4x - 4x -2y = 12 – 4x -2 -2 y = -6 + 2x
D U
4) Solve for y: 4x – 2y = 12
· -2
+ 4x
- 4x
÷ -2
- 4x x
-2y = 12 – 4x
y = x
or y = 2x - 6
Draw “the river”
Subtract 4x from both sides
Simplify
Divide both sides by -2
Does it simplify?
Yes!

19. 5) The formula for the volume of a rectangular prism is V = LWH
5) The formula for the volume of a rectangular prism is V = LWH. Which equation solves the formula for L?
L = V - WH
Answer Now

20. 6) The formula for the volume of a pyramid is V =
6) The formula for the volume of a pyramid is V = Which equation solves the formula for h?
h = 3Vb
Answer Now