Infinite and No Solution Equations

Simplify each equation. Tell whether the equation has one, no, or infinite solutions.

3x - 8 = 3(x - 4) + 1

• one

• no solutions

• infinite solutions

• x = 0

Simplify each equation. Tell whether the equation has one, no, or infinite solutions.

4x - 7 = 3(2x - 3) + 2 - 2x

• one

• no solutions

• infinite solutions

• x = 0

Simplify each equation. Tell whether the equation has one, no, or infinite solutions.

5x + 6 = 2 + 3x

• x = -2

• no solutions

• infinite solutions

• x = -4

Solve:

2x + 1 = 2x - 1

• No Solution

• x = 0

• Infinitely Many Solutions

• x = 1

Solve:

3x + 15 = 3(x + 5) - x

• No Solution

• x = 15

• Infinitely Many Solutions

• x = 0

Solve:

3x + 15 = 3(x + 5)

• No Solution

• x = 15

• Infinitely Many Solutions

• x = 5

Solve:

2x + 1 = 4x - 1

• x = 1

• x = 0

• Infinitely Many Solutions

• no solution

What is the solution to the equations?

• one solution
• no solution
• infinite solutions
• none of these

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

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

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