Multi-step inequalities

Solving Multi-step inequalities/ Resolver desigualdades de varios pasos

How to solve:

• Distribute / Distribuir

• Combine like terms/ combinar términos semejantes

• Gather Variables to one side/ Reúna las variables a un lado

• Add/subtract - Sumar/restar

• Divide/multiply - dividir/multiplicar

• Variable always on the left hand side/Variable siempre en el lado izquierdo

Remember

• Inequalities are solved just like equations

• But...

• Flip the sign if you multiply or divide both sides by a negative

• Las desigualdades se resuelven igual que las ecuaciones.

• Pero...

• Invierte el signo si multiplicas o divides ambos lados por un negativo

Multiple Choice

Solve/Resolver

8n - 6n > 24

• 
  

  $$n>12$$

• $$n<12$$

• $$n\ge12$$

Multiple Select

$$4\left(4n-3\right)\le-44$$  
After distributing, my inequality should look like what?

Después de distribuir, ¿cómo debería verse mi desigualdad?

• $$8n-3\le-44$$  

• $$8n-7\le-44$$  

• $$16n-12\le-44$$  

• $$16n-3\le-44$$  

Multiple Choice

Now solve 

$$16n-12\le-44$$  

• $$n\ge-2$$  

• $$n\le-2$$  

• $$n\ge2$$  

Multiple Choice

$$3\left(3+3n\right)>27$$  

• $$n>2$$  

• $$n<2$$  

• $$n\ge3$$  

Multiple Choice

$$33\le3\left(2+3p\right)$$  

• $$p<3$$  

• $$p<11$$  

• $$p\ge3$$  

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!!

¡Ahora juntemos todo! Distribuye, combina y resuelve!!

$$-3\left(2-3x\right)<-33$$  

• $$x<3$$  

• $$x>-3$$  

• $$x<-3$$