Solving Equations Using Algebra

 $If:\ \frac{2}{3}x\ -4=20$  

•  $Then:\ \frac{2}{3}x-4+4=20-4$  

•  $Then:\ \frac{2}{3}x+0=24$  

•  $Then:\ \frac{2}{3}x=24$  

•  $Then:\ \left(\frac{3}{2}\right)\frac{2}{3}x=\left(\frac{3}{2}\right)24$  

 $If:\frac{2}{3}x+0=24$ 

• $Then:\ \frac{2}{3}x-4+4=20-4$

•  $Then:\ \frac{2}{3}x-\frac{2}{3}=24-\frac{2}{3}$ 

•  $Then:\ \frac{2}{3}x=24$ 

• $Then:\ \left(\frac{3}{2}\right)\frac{2}{3}x=\left(\frac{3}{2}\right)24$

 $If:\ \frac{2}{3}x=24$ 

• $Then:\ \frac{2}{3}x-4+4=20-4$

• $Then:\ \frac{2}{3}x+0=24$

• $Then:\ \left(\frac{3}{2}\right)\frac{2}{3}x=\left(\frac{3}{2}\right)24$

•  $Then:\ \frac{2}{3}x-\frac{2}{3}=24-\frac{2}{3}$ 

 $If:\ \left(\frac{3}{2}\right)\frac{2}{3}x=\left(\frac{3}{2}\right)24$ 

• $Then:\ \frac{2}{3}x-4+4=20-4$

• $Then:\ \frac{2}{3}x+0=24$

•  $Then:\ \frac{2}{3}x=24$ 

• $Then:\ 1x=36$

 $If:\ 1x=36$  

 $Then:$  

Kym switched cell phone plans. She signed up for a new plan that will save her $3.50 per month compared to her

old cell phone plan. The cost of the new phone plan for an entire year is $294. How much did Kym pay per month

under her old phone plan?

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Name the justification for the following statement:

 $If:\ 12\left(x+9\right)=-108$  

 $Then:\ \left(\frac{1}{12}\right)12\left(x+9\right)=\left(\frac{1}{12}\right)\left(-108\right)$  

Name the justification for the following statement:

 $If:\ 1\left(x+9\right)=-9$  
 $Then:\ x+9=-9$  

Name the justification for the following statement:
 $If:\ x+9=-9$  

 $Then:\ x+9-9=-9-9$  

Name the justification for the following statement:

 $If:\ x+0=-18$  

 $Then:\ x=-18$