Ask a New Question
Menu

Directions: Use this worksheet to record your answers to the questions about linear

equations. When you are finished, save this worksheet with your answers and submit
it for a portfolio grade.
Investigate and explain the different number of solution an equation can have.

Question 1
Examine the six different equations that follow. Determine which equations have
one solution, no solution, or infinitely many solutions.
• Put a circle around the two equations that have infinite solutions.
• Put a square around the two equations that have no solution.
• Underline the two equations that have one solution.

2x+3=2x+7
7x+3=7x+3
4x+22=8x+10
5x+5=5x+4
3x+18=5x+8
3(4x+8)=4(3x+6)

1 answer

To analyze the equations for their number of solutions, let’s check each equation one by one:

  1. Equation: 2x + 3 = 2x + 7

    • Subtract 2x from both sides: 3 = 7
    • This is a false statement.
    • No solution. (Square)

  2. Equation: 7x + 3 = 7x + 3

    • Both sides are identical.
    • This is a true statement for all values of x.
    • Infinitely many solutions. (Circle)

  3. Equation: 4x + 22 = 8x + 10

    • Subtract 4x from both sides: 22 = 4x + 10
    • Subtract 10 from both sides: 12 = 4x
    • Divide by 4: x = 3
    • One solution. (Underline)

  4. Equation: 5x + 5 = 5x + 4

    • Subtract 5x from both sides: 5 = 4
    • This is a false statement.
    • No solution. (Square)

  5. Equation: 3x + 18 = 5x + 8

    • Subtract 3x from both sides: 18 = 2x + 8
    • Subtract 8 from both sides: 10 = 2x
    • Divide by 2: x = 5
    • One solution. (Underline)

  6. Equation: 3(4x + 8) = 4(3x + 6)

    • Expand both sides: 12x + 24 = 12x + 24
    • Both sides are identical.
    • This is a true statement for all values of x.
    • Infinitely many solutions. (Circle)

Here is the classification of the equations:

  • Infinitely many solutions:

    • 7x + 3 = 7x + 3 (●)
    • 3(4x + 8) = 4(3x + 6) (●)

  • No solution:

    • 2x + 3 = 2x + 7 (□)
    • 5x + 5 = 5x + 4 (□)

  • One solution:

    • 4x + 22 = 8x + 10 (____)
    • 3x + 18 = 5x + 8 (____)

Thus, your final answers should look like this:

  • Infinitely many solutions (circled):

    • 7x + 3 = 7x + 3
    • 3(4x + 8) = 4(3x + 6)

  • No solution (squared):

    • 2x + 3 = 2x + 7
    • 5x + 5 = 5x + 4

  • One solution (underlined):

    • 4x + 22 = 8x + 10
    • 3x + 18 = 5x + 8