MultiStep Inequalities

Solving Multi-Step Inequalities

Solving Multi-step inequalities

• very similar to solving multi-step equations

• combine like terms

• get all the variables on one side
  

• isolate the variables
  
  

Multiple Choice

Solve this

 $3x+4\le19$  

• x = 5

•   $x\ >5$  

•  $x\le5$  

Multiple Choice

How would you describe the answer to the previous question?

• All numbers below 5

• All numbers above 5

• All numbers less than or equal to 5

Sometimes you have to combine like terms before you can solve the inequality

Multiple Choice

 $8n-6n>24$ 

 What is your first step in solving this inequality?

• Subtract 8n on both sides

• Combine 8n and -6n

• Add 6n on both sides

Multiple Choice

What is the answer to this inequality?

8n-6n>24

• 
  

  $n>12$

• $n<12$

• $n\ge12$

Sometimes you must distribute first, and then combine like terms before you can solve the inequality. 

Fill in the Blank

 $4\left(4n-3\right)\le\left(-44\right)$  
The first thing I need to do is distribute the ___ to 4n and 3.

Multiple Select

 $4\left(4n-3\right)\le\left(-44\right)$  

After distributing, my iniquality should look like what?

•  $8n-3\le-44$  

•  $8n-7\le-44$  

•  $16n-12\le-44$  

•  $16n-3\le-44$  

Multiple Choice

Now solve 

 $16n-12\le-44$  

•  $n\ge-2$  

•  $n\le-2$  

•  $n\ge2$  

Now try these......

Multiple Choice

 $3\left(3+3n\right)>27$  

•  $n>2$  

•  $n<2$  

•  $n\ge3$  

Multiple Choice

 $33\le3\left(2+3p\right)$  

•  $p<3$  

•  $p<11$  

•  $p\ge3$  

Something interesting happens when you multiply or divide both side of an inequality by a negative number.

Open Ended

Take for example....

 $3>1$ 

 We know this is true. 3 is greater than 1. But what if we multiplied both sides by -1....

 $\left(-1\right)3>\left(-1\right)1$ 

 Then we get this.... $-3>-1$ 
 THIS ISN'T TRUE!!!

The only way to make it true would be to flip around the inequality like this..
 $-3<-1$  

Multiple Choice

Solve this......

 $3\left(3-3n\right)<36$  

•  $n<-3$  

•  $n>-3$  

•  $n\le-3$  

Fill in the Blank

Whenever I multiply or divide both sides of an inequality by a NEGATIVE, I must ____ the inequality sign.

Multiple Choice

Now lets put it all together! Distribute, combine and solve!!

 $-3\left(2-3x\right)<-33$  

•  $x<3$  

•  $x>-3$  

•  $x<-3$  

Poll

How do you feel about solving inequalities now?

• Great

• Good

• Ok

• Not good