All the Parts of an Equation

All the Parts of an Equation

Understand all the parts of the equation before solving it.

Equations have equal signs

•  $2c-6=28$  

•  $\frac{4}{5}b+9=11$  

•  $7a=49$  

•  $-8-m=31$  

•  $\frac{x}{6}=23$  

Multiple Choice

Which of the following is not an equation?

• 
  

  $\frac{2}{3}y=8$
  

• $15m\ +8$

• $9x-11=7$

• $-5-34c=60$

Equations have variables, coefficients and constants

• variables are letters that hold a numerical value

• a constant is a number on its own

• a coefficient is a number with a variable

 $-n+16=-11$  

•  $-n$  is the variable term; the coefficient $-1$   is with the variable

• the coefficient is 

•  $16$  is constant on the side of the equation with the variable

•  $-11$   is a constant

Equations have variables

• variables are letters that hold an unknown value

• it is your job to find that value of that variable

• variables can be any where in the equation

• the following equation has a variable of $c$   

•  $-15=3c-12$  

Multiple Choice

 $\frac{m}{21}=8$  What is the variable?

•  $8$  

•  $21$  

•  $m$  

•  $\frac{1}{21}$  

Multiple Choice

 $-9r-19=110$  

What is the variable?

•  $110$  

•  $-9$  

•  $9r$  

•  $r$  

Poll

I feel confident I can find the variable every time.

• Yes

• No

Equations are like Ogers

When solving an equation start on the side with the variable

 $-3n+16=-34$  

• The variable is  $n$  so start on that side of the equation

•  $n$  is on the inside of the onion

• peel away the addition or subtraction

• then peel away the coefficient to get to the variable

Start on the side with the variable

 $-3n+16=-34$  

• The variable is  $n$  so start on that side of the equation

•  $n$  is on the inside of the onion

• peel away the addition or subtraction

• the variable is  $n,$  so the number separated by addition /subtraction sign is  $16$  

First find the variable, then the constant term is the number separated by a addition or subtraction symbol. 

 $-2=-9k+22$  

• The variable is ?

• there is an addition sign before the constant of  $22$  

• remember the  $-9$  is with the variable don't get them confused

Multiple Choice

In terms of the variable what is the constant?

 $9x-3=12$  

•  $9$  

•  $9x$  

•  $-3$  

•  $12$  

Fill in the Blanks

In terms of the variable what is the constant?

 $1-4m=-85$  

Fill in the Blanks

In terms of the variable what is the constant?

 $-5=-2x+7$  

Order of operations

When solving an equation work backwards

• S ubtraction or Addition

• M ultiplicatin or Division

• 
  

• 
  

Poll

Who wants to see the video again?

• Yes

• No

Fill in the Blanks

When solving an equation work

Operations and their opposites/inverses

• Addition is the opposite of subtraction

• Subtraction is the opposite of addition

• positive is the opposite of negative

• negative is the opposite of positive

• multiplication is the opposite of division

• division is opposite of multiplication

 $5x-16=9$  

• First find the variable

• The variable is x

• Start on the side with the x peel away the  $-16$  

• the inverse is  $+16$  

• So add 16 to both sides of the =

• 
  

 $-19=\frac{2}{3}m-21$  

• Find the variable.

• The variable is  $m$  

• Start on the side with the  $m$ , peel away the  $-21$  

• the inverse of  $-21$  is  $+21$  

• add  $21$  to sides of the  $=$   sign

Fill in the Blanks

In the equation $10=-3j+17$  What is the variable?

Multiple Choice

In the equation $10=-3j+17$    the variable is j what needs to be peeled away first?

•  $10$  

•  $7$  

•  $-3$  

•  $17$  

Multiple Choice

In the equation $10=-3j+17$    the variable is j what is the inverse of +17?

•  $-10$  

•  $+3$  

•  $-17$  

•  $+17$  

The coefficient ...

• is the number before the variable

• the coefficient is multiplied by the variable

• the coefficient can be negative or positive

• the coefficient can be a fraction or a decimal

• us the inverse of the multiplication to isolate the variable

• the inverse of multiplicaion is division

Multiple Choice

In the equation

 $-20f\ +5=45,$  what is the variable term (the term that contains the variable)

•  $45$  

•  $-20f$  

•  $5$  

•  $-20$  

Multiple Choice

In the equation

 $-20f\ +5=45,$  what is the coefficient?

•  $45$  

•  $-20f$  

•  $5$  

• -20

Multiple Choice

 $\frac{4}{5}d\ -27\ =9$  What is the coefficient of the variable  term?

•  $\frac{4}{5}$  

•  $4$  

•  $7$  

•  $-27$  

•  $9$  

Variables can also be divided by a number

• 
  
   $\frac{m}{6}$  
  

•  $\frac{r}{18}$  

•  $-\frac{y}{9}$