Solving Equations Special Cases

Solve the following equation:

4 − 6x − 2= −2(3x − 1)

• no solution

• infinitely many solutions

• x = ⅓

• x = 4

Rate your level of understanding for solving equations with one solution, infinitely many solutions, and no solutions.

• I don't understand what to do.

• I somewhat understand, but I need more practice.

• I somewhat understand, but I need additional help.

• I understand what to do and feel confident.

What does it mean when an equation has no solution?

• the equation will NEVER be true when any value is substituted in for the variable

• the equation is always TRUE when any value is substituted in for the variable

• only ONE solution will make the equation true

Solve the equation and state if it has one, many, or no solutions.

10x - 9 = 2x + 63

• x = 9, one solution

• x = 8, one solution

• Many Solutions

• No solution

Solve the equation and state if it has one, many, or no solutions.

11x - 5 = 8x + 31

• x = 12, one solution

• x = 9, one solution

• Many Solutions

• No solution

Solve the equation and state if it has one, many, or no solutions.

9y + 2 = 3(3y + 2) - 4

• One solution

• Many Solutions

• No Solution

Solve the equation and state if it has one, many, or no solutions.

3(2x - 8) = 2(3x - 12)

• One solution

• Many Solutions

• No Solution

Solve the equation and state if it has one, many, or no solutions.

5(3x - 6) = 3(5x - 10)

• One solution

• Many Solutions

• No Solution

Solve the equation and state if it has one, many, or no solutions.

2(x - 8) = 7 + 2x

• One solution

• Many Solutions

• No Solution

Solve the equation and state if it has one, many, or no solutions. 4(r + 2) - 3 = 4r - 11

• One solution

• Many Solutions

• No Solution