Solving Equations Special Cases

10x + 3 + 3x = 5x + 1 + 8x + 2

• x = -3

• x = 3

• infinitely many solutions

• no solutions

3x + 1 + 2x = 4x − 2 − 7x + 7

• x = 2

• x = ½

• infinitely many solutions

• no solutions

If while solving an equation your solution appears like so, 3 = 4, how many solutions do you have?

• One Solution

• No Solutions

• Infinitely Many Solutions (all real numbers)

What does it mean when an equation has infinitely many solutions?

• "To infinity and beyond"

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

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

• only ONE solution will make the equation true

What does it mean when an equation has one solution?

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

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

• only ONE solution will make the equation true

• infinitely many solutions

• no solution

• x = 0

• x = -80

Determine whether the equation below has one solution, no solutions, or infinitely many solutions.

• Infinitely Many Solutions

• One solution

• No solution

Which answer best describes the solution to the following equation?

• No solution

• 0

• 1

• Infinitely many solutions

Solve for x and type the number only in the blank.

Solve for x:
5x - 14 = 8x + 4