Lesson 17

Number of Solutions in One-Variable Equations

  • Let's look at the number of solutions an equation may have.

17.1: Notice and Wonder: Three Graphs

What do you notice? What do you wonder?

Coordinate plane, x, 0 to 10 by 2, y, negative 5 to 5 by 2. Line graphed through 0 comma negative 5 and 2 comma negative 2.
Coordinate plane, x, 0 to 10 by 2, y, negative 5 to 5 by 2. Line through 0 comma negative 5 and 2 comma negative 2. Second line through 2 comma 2 and 5 comma 0.
Coordinate plane, x, 0 to 10 by 2, y, negative 5 to 5 by 2. Two lines. First, through 0 comma negative 5 and 2 comma negative 2. Second, through 2 comma negative 4 and 4 comma negative 1.

17.2: How Many Answers?

How many values of \(x\) make each equation true?

  1. \(3x + 1 = 10\)
  2. \(2x + 12 = 2x + 10 + 2\)
  3. \(2x = x + 2\)
  4. \(3(x+4) = 3x + 4\)
  5. \(\frac{2x+6}{2} = x + 6\)
  6. \(0 = 0\)
  7. \(x + 3x - 4 = 7(x - \frac{4}{7})\)
  8. \(0 = 6\)

With your partner, discuss what you notice about the equations based on the number of solutions they have.

17.3: Write, Trade, Check

  1. Write an equation that has either 1, 0, or infinite solutions.
  2. Trade your equation with your partner. Solve the equation you are given and determine the number of solutions.
  3. Take turns explaining your reasoning with your partner.
  4. Repeat the process with a new equation.

Summary