Number of Solutions of One Variable

What is the solution to the equations?

• one solution

• no solution

• infinite solutions

• none of these

Solve:
2x + 1 = 2x - 1

• No Solution

• x = 0

• Infinitely Many Solutions

How many solutions? 4x - 3 = 3(2x + 3)

• one solution

• no solution

• infinitely many solutions

An equation has one solution if...

• The variable is eliminated and we are left with something false (like 2=3).

• The variable is eliminated and we are left with something true (like 2=2).

• We can find the exact value of the variable.

An equation has no solution if...

• The variable is eliminated and we are left with something false (like 2=3).

• The variable is eliminated and we are left with something true (like 2=2).

• We can find the value of the variable.

If an equation has no solution, it is ___________ true.

• Always

• Sometimes

• Never

An equation has infinitely many solutions if...

• The variable is eliminated and we are left with something false (like 2=3).

• The variable is eliminated and we are left with something true (like 2=2).

• We can find the value of the variable.

How many solutions does this equation have?

• Always

• Sometimes

• Never

How many solutions does this equation have?

• Always

• Sometimes

• Never

If an equation has infinitely many solutions, it is ___________ true.

• Always

• Sometimes

• Never