Determining the Number of Solutions of an Equation

Level 2:

Determine whether the equation has one, no, or infinite solutions.

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

• one

• no solutions

• infinite solutions

Level 3

Determine the number of solutions:

14 - 2 (3p + 1) = 6(4 + p)

• No Solution

• One Solution

• Infinite Solutions

Level 3

Determine the number of solutions:

8z - 22 = 3(3z + 11) - z

• No Solution

• One Solution

• Infinite Solutions

Level 3

Determine the number of solutions

6x - 18 = 4(2x - 3) - (2x + 6)

• No Solution

• One Solution

• Infinite Solution

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:

8x + 4(4x − 3) = 4(6x + 4) − 4

• one solution

• no solution

• infinitely many solutions

Level 3

Determine the number of solutions

6x - 18 = 4(2x - 3) - (2x + 6)

• No Solution

• One Solution

• Infinite Solution

Level 3

Determine the number of solutions.

12(x + 3) = 4(2x + 9) + 4x

• No Solution

• One Solution

• Infinite Solutions

Level 3

Determine the number of solutions

2 (15c + 8) = 9(2c + 4) - (3c + 2)

• No Solution

• One Solution

• Infinite Solution

Solve the equation.

5 + 2(n + 1) = 2n

• The equation is an identity.

• The equation has exactly one solution, n = 7.

• The equation has no solution.

• The equation has exactly one solution, n = 0.