Equations

Equations

What is  an Equation?

Poll

What do you know about expressions and equations? Pick all that apply.

• They are scary math terms

• An expression is a math sentence with a clause (equal sign)

• An equation is a math sentence without a clause (equal sign)

• An equation is a math sentence with a clause (equal sign)

• An expression is a math sentence without a clause (equal sign)

Equations

You are very familiar with these and you don't even realize it. Equations are math sentences with a clause aka an equal sign i.e. 2+4=6

Expressions

You have seen these but you have always turned them into equations. Expressions are math sentences without a clause aka equal sign i.e. 49+31

Multiple Choice

Is this an expression or an equation  $$52\times12$$ ?

• Expression

• Equation

Multiple Choice

Is this an expression or an equation  $$12-4=8$$ ?

• Expression

• Equation

Multiple Choice

Is this an expression or an equation  $$4+x$$ ?

• Expression

• Equation

Multiple Choice

Is this an expression or an equation  $$25x=175$$ ?

• Expression

• Equation

When Solving for x.

To solve for x there must be an equation. There are 2 types single step and multi-step equations. Let's explore them...

Single Step

• This occurs when there is only one math operation to the equation. To solve you must do the opposite of the operation that is there.

• 2x=6     -->    2x/2=6/2    -->   x=3

• Multiplying means you must divide

• Dividing means you must multiply
  

• Adding means you must subtract

• Subtracting means you must add

Poll

What operation do you need to do to solve for x in $$12x=108$$ ? 

• Add

• Multiply

• Subtract

• Divide

Multiple Choice

Solve for x in $$12x=108$$ . 

• 9

• 8

• 10

• 5

Poll

What operation do you need to do to solve for x in $$18+x=32$$ ? 

• Add

• Multiply

• Subtract

• Divide

Multiple Choice

Solve for x in $$18+x=32$$ .

• 18

• -18

• 14

• -14

Poll

What operation do you need to do to solve for x in $$x-24=-7$$ ? 

• Add

• Multiply

• Subtract

• Divide

Multiple Choice

Solve for x in $$x-24=-7$$ .

• 12

• -12

• -17

• 17

Fill in the Blanks

What operation do you need to do to solve for x in $\frac{x}{13}=3$ ? 

Fill in the Blanks

Solve for x in $\frac{x}{13}=3$ ? 

Fill in the Blanks

$15x=-105$  

Multi-Step

• This is when more than one mathematical operation exists within the equation.

• 2x+3-x=5   -->   x+3=5   -->   x=2

• The first thing is to combine like terms (these are parts with the same variable), if needed

• Once once terms are combined you will work backwards from PEMDAS to SADMEP 

• Reverse all operations in reverse operational order to get x by itself

• Like Terms-->    4a-8a-7+15=-16

• -->   -4a+8=-16

• Reverse Operations-->   -4a+8-8=-16-8

• -->   -4a=-24   -->   -4a/-4=-24/-4

• Now the variable is by itself-->  a=3

​Let's take a look at the steps

Poll

What is the first step 5x+9=34?

• Combine Like Terms

• Reverse Operations (SADMEP) No like terms

Fill in the Blanks

Solve for x in the equation 5x+9=34?

Poll

What is the first step in solving this equation $$4x-11+3x=94$$ ? 

• Combine Like Terms

• Reverse Operations (SADMEP)

Fill in the Blanks

Solve $4x-11+3x=94$

Poll

$$3\left(x-1\right)+x=-23$$  

• Combine Like Terms

• Reverse Operations (SADMEP)

• Distribute the 3

What to do with Parenthesis?

When there are groupings involve you will want to simplify those first. The idea is to make put in a format to easily combine the like terms.

Multiple Choice

$$3\left(x-1\right)+x=-23$$  What is x?

• -5

• 8

• 3

• -7