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Grade 6 · lesson 3 of 4

Represent a Strict Inequality and Its Boundary

Read the comparison sign and the supplied domain.

About 20 minutes, plus any extended practice

Download the grade pack

Supplied materials

  • Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
  • Supplied worked-case record: For real x>5, put an open circle at five and shade right.
  • All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.

Learn the idea

A strict inequality such as x>c excludes its boundary c. Over real numbers, it has infinitely many solutions on one side of the boundary. An open circle shows exclusion on a number line. A whole-number context restricts which points are allowable, so its solution list may be discrete instead.

Read the comparison sign and the supplied domain. Test values by substitution, exclude the boundary for a strict sign, and describe the corresponding open-circle direction. Do not silently replace a strict inequality with an inclusive condition.

Check whether the boundary is included by the sign. Real-number and whole-number domains give different allowable solution sets. Mark the boundary and label whether it is open or closed before choosing a direction.

  1. Mark the boundary and label whether it is open or closed before choosing a direction.
  2. Work through the supplied example and label what each number or attribute represents.
  3. Read the comparison sign and the supplied domain.
  4. Answer the check, then try the three changed-input practice questions and explain one correction.
Worked example

See the method in action

For real x>5, put an open circle at five and shade right. Values 5.1 and 8 satisfy, while five does not. If x counts whole packets, the valid quantities are 6,7,8,... . The real-number diagram and whole-number list express different domain restrictions. Check whether the boundary is included by the sign. Real-number and whole-number domains give different allowable solution sets. Mark the boundary and label whether it is open or closed before choosing a direction.

Your turn

Check your reasoning

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Helpful tips
  • Check whether the boundary is included by the sign.
  • Real-number and whole-number domains give different allowable solution sets.
For real numbers x>3, which supplied value is a solution?

Feedback appears here after you check. This is practice, not a graded school assessment.

See the answer and explanation

3.5

A strict greater-than condition excludes the boundary and accepts larger values.

Take it further

Represent real t<2. Expected: open circle at two, shading left; 2 excluded.

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More practice: try new cases

Choose an answer for each problem. Explain your method on paper, then use the feedback to decide what to revisit.

More practice: try new cases
1. For real numbers x>4, which supplied value is a solution?
Need a hint?
  • Check whether the boundary is included by the sign.
  • Real-number and whole-number domains give different allowable solution sets.
2. For real numbers x>5, which supplied value is a solution?
Need a hint?
  • Check whether the boundary is included by the sign.
  • Real-number and whole-number domains give different allowable solution sets.
3. For real numbers x>6, which supplied value is a solution?
Need a hint?
  • Check whether the boundary is included by the sign.
  • Real-number and whole-number domains give different allowable solution sets.

Your choices are temporary. Feedback appears after you check all the answers.

Nothing here is saved to an account or sent to a teacher. Keep your own notes or download them before leaving. The score describes these questions; it does not certify subject mastery.

Check the subject sources

These LifeStarter passages, scenarios and exercises are authored for this Academy with AI assistance and review. External resources keep their publishers’ terms. A grade label suggests a starting level; it does not establish alignment with your school’s complete requirements.