Determine Solution to an Equation

Solve the equation.

3x + 15 = 3(5 + x)

• There is no solution.

• There is only one solution, x = 15.

• The solution is all real numbers.

• Cannot be determined

Which of the following also means "infinite solutions"?

• Identity

• No Solution

• Infinitely Many Solutions

How many solutions does the following equation have:

−16 + 5n = −7(−6 + 8n) + 3

• one solution

• no solution

• infinitely many solutions

Determine the number of solutions the following equation has:

−5 + 5(n − 7) = −40 + 5n

• one solution

• no solution

• infinitely many solutions

Determine the number of solutions the following equation has:

8x + 4(4x − 3) = 4(6x + 4) − 4

• 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 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

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)