Solutions of an Equation

What does it mean for an equation to have 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 ONE number will make the equation true

Determine the number of solutions the following equation has:

−5 + 5(n − 7) = −40 + 5n

• one solution

• no solution

• infinitely many solutions

6x + 9 – x = 3x + 9 + x

• No Solution

• One Solution

• Infinite Solutions

What does it mean for an equation to have 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 ONE number will make the equation true

What does it mean for an equation to have no 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 ONE number will make the equation true

Determine which equation has infinitely many solutions.

• 3(2x - 1) = 3(4x - 1)

• 3(2x + 6) = 2(3x + 9)

• 2(3x + 4) = 3(2x + 3)

• 6(x - 5) = 6(3x - 4)

Solve the equation
4x - 5x + 9 =5x - 9

• x = -3

• x = 9

• x = 3

• x = -9

8v - 4(v + 8) = 8

• 2

• 10

• 4

• -4 

Solve.

• -1

• Infinitely many solutions

• No solution

• 0

Solve.  

• 7

• No solution

• All real numbers

• 0