Solving Multi-Step Equations (with Special Cases)

What is the first step in solving the equation

 $2a-4(a-5)=10$  

• Add 4 to both sides

• Add the 2a and a 

• Distribute 4 to a and -5

• Distribute -4 to a and -5

Tags

CCSS.8.EE.C.7B

Solve:
 $2+14a=-8+9a$  

•  $a=-2$  
  

•  $a=3$  
  

•  $a=5$  
  

•  $a=-10$  
  

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

Solve:
 $22+2a=37+6+a$  

•  $a=21$  
  

•  $a=-21$  
  

•  $a=5$  
  

•  $a=6$  
  

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

Identify if this equation has one solution, infinitely many solutions or no solution.

 $-3x+1=x+9-4x$  

• one solution

• infinitely many

• no solution

Tags

CCSS.8.EE.C.7A

Solve:

 $5x+4=5x−3$  

•  $x=4$  
  

•  $x=-3$  
  

• infinitely many solutions

• no solutions

Tags

CCSS.8.EE.C.7A

Solve:

 $\frac{1}{2}\left(4y−8\right)=\frac{2}{5}\left(5y−10\right)$  

•  $y=0$  
  

•  $y=-3$  
  

• infinitely many solutions

• no solutions

Tags

CCSS.8.EE.C.7B

What does it mean when an equation has one solution?

• The equation is always TRUE when any value is substituted in for the variable.

• The equation will NEVER be true no matter what value is substituted in for the variable.

• Only ONE solution will make the equation true.

• The equation cannot be solved.

Tags

CCSS.8.EE.C.7A

What does it mean when an equation has infinitely many solutions?

• "To infinity and beyond."

• The equation is always TRUE when any value is substituted in for the variable.

• The equation will NEVER be true when any value is substituted in for the variable.

• Only ONE solution will make the equation true.

Tags

CCSS.8.EE.C.7A

Solve:
 $-\left(8x-4\right)-\left(6x-2\right)=6-4x+5x$  

• infinitely many solutions

• no solution

•  $x=0$  

•  $x=-2$  
  

Tags

CCSS.8.EE.C.7A

What does it mean when an equation has no solution?

• The equation is always TRUE when any value is substituted in for the variable.

• The equation will NEVER be true no matter what value is substituted in for the variable.

• Only ONE solution will make the equation true.

• The equation cannot be solved.

Tags

CCSS.8.EE.C.7A