How Many Solutions?

How Many Solutions?

A review of the 3 types of solutions to equations

Infinitely Many Solutions

• True mathematical statement

• Example 3=3

• The coefficients on the variables will be the SAME on both sides of the equation, and the remaining numbers to be the SAME.

• Example: 4x+15=4x+15

One Solution

• Solve for the variable, ends with the variable equal to ONE number.

• Ex. x=3

• The coefficients on the variables will be DIFFERENT

• Ex. 5x+30=7x+30

No Solution

• Ends with a FALSE mathematical statement

• Ex. 4=8

• The coefficient on the variable will be the SAME, much like with a true statement. But, the remaining numbers will be DIFFERENT.

• Ex. -7x+10= -7x+15

Multiple Choice

3x+2=2+3x

• One Solution

• No Solution

• Infinitely Many

Multiple Choice

2(x+3)=2x+6

• One Solution

• No Solution

• Infinitely Many

Multiple Choice

-3x-5+5x=2(x+7)

• One Solution

• No Solution

• Infinitely Many

Multiple Choice

10+3x=5(x-2)

• One Solution

• No Solution

• Infinitely Many

Multiple Choice

-x-(-10)= -(x-10)

• One Solution

• No Solution

• Infinitely Many

Multiple Choice

-6+3x-(-8x)=12x+(-3)-5x

• One Solution

• No Solution

• Infinitely Many

Multiple Choice

6(x+6)-6x=-6(x-6)+6x

• One Solution

• No Solution

• Infinitely Many

Multiple Choice

-8(x-(-8))+8x=8(x+8)+8x

• One Solution

• No Solution

• Infinitely Many