Ch. 2 Review

Ch. 2 Review

One Step Equations

• Inverse operations undo

• inverse of addition is subtractions

• inverse of subtraction is addition

• inverse of multiplication is division

• inverse of division is multiplication

Multiple Choice

 $5\ +\ x\ =7$  

•  $x=2$  

•  $x=-2$  

•  $x=12$  

Multiple Choice

 $\frac{h}{3}=4$  

•  $h=\frac{4}{3}$  

•  $h=\frac{3}{4}$  

•  $h=12$  

•  $h=1$  

Two Step Equations

• Add or Subtract First

• Then Multiply or Divide

Multiple Choice

What is the first step: $2x-3=4$  

• subtract 3 from both sides

• add 3 to both sides

• multiply both sides by 2

• divide both sides by 2

Multiple Step Equations

• Distribute

• Combine Like Terms (gather like terms on EACH side of the = )

• Move Variables (letters) to One Side of the = by Adding or Subtracting the Smaller Coefficient

• Move Constants (numbers) to the Other Side of the = by Adding or Subtracting

• Multiply or Divide to Isolate the Variable

Open Ended

What is the FIRST step to solve this equation: $2\left(4x-5\right)+x=4\ +2x$  

Open Ended

What is the NEXT step to solve this equation:
 $8x-10+x=4+2x$  

Multiple Choice

What do we get when we combine like terms for this equation: $8x-10+x=4+2x$  

•  $9x-10=4+2x$  

•  $7x-10=4+2x$  

Poll

Which variable should we move?

• 9x

• 2x

Literal Equations

• Follow the SAME rules for solving equations

• The solution will have variables on both sides of the =

• Usually formulas

Multiple Choice

 $d=rt$  
Solve for  $r$  

•  $r=dt$  

•  $r=d-t$  

•  $r=d+t$  

•  $r=\frac{d}{t}$  

Poll

 $\frac{\left(a-3\right)}{b}=c$  

What is the first step to solve for a:

• add 3 to both sides

• multiply both sides by b

Poll

 $\left(a-3\right)=bc$  
What is the next step to solve for a

• divide by bc

• add 3 to both sides

• subtract a from both sides

Open Ended

 $\frac{\left(a-3\right)}{b}=c$  

Solve for a

Absolute Value Equations

• Treat the |absolute value| like it was a variable and get it isolated (by itself on one side of the = )

• If your absolute value = a negative, you have NO solution

• If your absolute value = 0, you only have ONE solution

• If your absolute value = a positive, you need to create 2 separate equations and will have TWO solutions

Multiple Choice

Do you have no, one or two solutions.... $\left|x+5\right|-10=-20$  

• no

• one

• two

Poll

What is the first step to solve: $3\left|x-2\right|+4=-2$  

• Distribute 3 to the absolute value

• Subtract 4 from both sides

• Divide 3 from both sides

• Add 4 to both sides

Poll

What is the next step to solve: $3\left|x-2\right|=2$  

• Distribute 3 to the absolute value

• Divide both sides by 3

• Add 3 to both sides

• Subtract 3 from both sides

Poll

How many solutions will this equation have? $\left|x-2\right|=6$  

• No solutions

• One solution

• Two solutions

Open Ended

 $\left|x-2\right|=6$  What are your final solutions?

Poll

How confident are you solving equations?

• I am a GENIUS - 100% here I come!

• I am Oh Kay - I will be GREAT after doing my Deltamath

• I am Struggling Stan - I'm going to come to Academic Support today at 1:45 (Zoom)