Types of Solutions

Types of Solutions

One Solution

4x = 32

This equation would only have 1 solution. 8 is the only number that would make this equation true and balance the scale.

Infinite Solutions

x = x

This equation would only have infinite solutions. Any number would make this equation true and balance the scale, because both sides are identical.

We would say this has infinite solutions, or the solution is All Real Numbers, or Identity

No Solutions

20 + x = 13 + x

This equation would only have no solution. There isn't any number that would make this equation true and balance the scale, because if we removed the x, we would have 20 = 13.

We would say this has no solution.

Multiple Choice

 $1+8x+9=-20+2x$  

• x = -5

• x = 5

• No Solution

• Infinite Solutions

Multiple Choice

 $2\left(5x-2\right)=-4+10x$  

• No Solution

• Infinite Solutions

•  $x=-8$  

•  $x=12$  

Multiple Choice

 $3\left(4-5x\right)=-2-15x$  

• No Solution

• Infinite Solutions

•  $x=14$  

•  $x=10$  

Multiple Choice

 $-24+20x=24+8x$  

•  $x=4$  

•  $x=-2$  

• No Solution

• Infinite Solutions

Multiple Choice

 $7x-3=-3+7x$  

• No Solution

• Infinite Solutions

•  $x=0$  

•  $x=6$  

Multiple Choice

 $2x+1=2x-1$  

• No Solution

• x = 0

• Infinite Solutions

• x = 2

Multiple Choice

 $-1+2x=6x+11$  

• x = -3

• x = 3

• No Solution

• Infinite Solutions

Multiple Choice

 $6x+5=8+4x+2x$  

• No Solution

• Infinite Solutions

•  $x=3$  

•  $x=13$  

Multiple Choice

 $-2-2x+7x=3$  

•  $x=1$   

•  $x=5$  

• No Solution

• Infinite Solutions

Multiple Choice

 $5\left(2+x\right)=45+5x$  

• No Solution

• Infinite Solutions

•  $x=35$  

•  $x=55$  

Multiple Choice

 $-2\left(x+11\right)=-18$  

•  $x=-2$  

•  $x=2$  

• No Solution

• Infinite Solutions

Multiple Choice

 $-2x+5=-2x+5$  

• No Solution

• Infinite Solutions

•  $x=10$  

•  $x=-20$