Infinite Solution, One Solution, No Solution

What is the definition of one solution?

• no matter what constant is substituted in for the variable, the equation is ALWAYS true

• no matter what constant is substituted in for the variable, the equation will NEVER be true

• only this ONE solution will make the equation true

What is the definition of no solution?

• no matter what constant is substituted in for the variable, the equation is ALWAYS true

• no matter what constant is substituted in for the variable, the equation will NEVER be true

• only this ONE solution will make the equation true

What is the definition of infinite solutions?

• no matter what constant is substituted in for the variable, the equation is ALWAYS true

• no matter what constant is substituted in for the variable, the equation will NEVER be true

• only this ONE solution will make the equation true

3r - 5 = 2r

• No solution

• Infinitely many solutions

• r = 5

Simplify each equation. Tell whether the equation has one, no, or infinite solutions.
5x + 6 = 2 + 3x

• one

• no solutions

• infinite solutions

14 - 2 ( 3p + 1) = 6 ( 4 + p)

• No Solution

• One Solution

• Infinite Solutions

8z - 22 = 3 ( 3z + 11) -z

• No Solution

• One Solution

• Infinite Solutions

12 (x + 3 ) = 4 (2x + 9 ) +4x

• No Solution

• One Solution

• Infinite Solutions

6x - 18 = 4(2x - 3) - (2x + 6)

• No Solution

• One Solution

• Infinite Solution

7x + 3 = 5(2x + 5) - (3x + 22)

• No Solution

• One Solution

• Infinite Solution