Lesson 19

Queuing on the Number Line

  • Let’s use number line to reason about inequalities

19.1: Notice and Wonder: Shaded Number Line

What do you notice? What do you wonder?

\(4>x\)

Number line, negative 10 to 10 by ones. Open circle at 4, line continues left.

19.2: Pick a Number

For each expression, pick a number you would like to evaluate, and tell whether it makes the inequality true. Be prepared to explain what made you choose your number.

  1. \(\frac43y+10>19\)
    1. Pick a number you would like to test in place of \(y\): -1, 0, 1, 3, 4, or 5. Explain why you chose your number.

    2. Does your number make the inequality true?

    3. What is a different number that is definitely a solution? How do you know?

    4. What is a different number that is definitely not a solution? How do you know?

  2. \(2.954x-14.287<13.89\)
    1. Pick a number you would like to test in place of \(x\): -1, -0.5, 0, 0.5, 1, 3, 10, or 1,000. Explain why you chose your number.

    2. Does your number make the inequality true?

    3. What is a different number that is definitely a solution? How do you know?

    4. What is a different number that is definitely not a solution? How do you know?

  3. \(10-3y<5\)
    1. Pick a number you would like to test in place of \(y\): -100, -3, -1, 0,\(\frac13\), \(\frac53\), 33, or 100. Explain why you chose your number.

    2. Does your number make the inequality true?

    3. What is a different number that is definitely a solution? How do you know?

    4. What is a different number that is definitely not a solution? How do you know?

  4. \(\frac{10x}{4} > \frac{3x}{5}\)
    1. Pick a number you would like to test in place of \(x\): -10, -5, -4, 0, 4, 5, 10, or 20. Explain why you chose your number.

    2. Does your number make the inequality true?

    3. What is a different number that is definitely a solution? How do you know?

    4. What is a different number that is definitely not a solution? How do you know?

19.3: Matching Words and Symbols

For each inequality, write 3 values that make the inequality true, write 3 values that make it false, and choose a verbal description that matches the inequality.

  1. \(x > 13.5\)
    1. Three values that make it true:
    2. Three values that make it false:
    3. Which verbal description best matches the inequality?
      1. \(x\) is less than 13.5
      2. \(x\) is greater than 13.5
      3. 13.5 is greater than \(x\)
  2. \(\text- 27 < x\)
    1. Three values that make it true:
    2. Three values that make it false:
    3. Which verbal description best matches the inequality?
      1. \(x\) is less than -27
      2. \(x\) is greater than -27
      3. -27 is greater than \(x\)
  3. \(x \geq \frac12\) and \(x \leq 2.75\)
    1. Three values that make it true:
    2. Three values that make it false:
    3. Which verbal description best matches the inequality?
      1. \(x\) is between \(\frac12\) and 2.75
      2. 2.75 is less than \(x\) is less than \(\frac12\)
      3. \(x\) is greater than \(\frac12\)
  4. \(x\geq \text-\frac{19}{4}\) and \(x \leq \frac12\)
    1. Three values that make it true:
    2. Three values that make it false:
    3. Which verbal description best matches the inequality?
      1. \(x\) is between \(\frac12\) and \(\text{-}\frac{19}{4}\) 
      2. \(x\) less than \(\text-\frac{19}{4}\)
      3. \(x\) is between \(\text-\frac{19}{4}\) and \(\frac12\)

Summary