Determining Number of Solutions

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

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

• one

• no solutions

• infinite solutions

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

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

• one

• no solutions

• infinite solutions

Solve:
2x + 1 = 2x - 1

• No Solution
• x = 0
• Infinitely Many Solutions

Solve:
3x + 15 = 3(x + 5)

• No Solution
• x = 15
• Infinitely Many Solutions

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

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

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 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 solution to this equation?

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