Solving Equations with One Solution, No Solution, Infinite Solutions

What is the solution to this equation?

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

What is the definition of one solution?

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

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

• only this ONE number will make the equation true

What is the definition of no solution?

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

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

• only this ONE number will make the equation true

What is the definition of infinitely many solutions?

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

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

• only this ONE number will make the equation true

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

3r - 5 = 2r

• No solution
• Infinitely many solutions
• r = 5

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

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

• one

• no solutions

• infinitely many solutions

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

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

• one

• no solutions

• infinitely many solutions

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

• one
• no solutions
• infinitely many solutions