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Finding an integer solution when the boundary is fractional

Finding an integer solution when the boundary is fractional.

  • Add or subtract the same amount on both sides without changing the inequality sign.
  • Multiplying or dividing both sides by a negative number reverses the inequality sign.
  • Every condition must hold. Use open endpoints for < or >, and closed endpoints for ≤ or ≥.

Example 1

Find the greatest integer satisfying the inequality.

Take the greatest integer strictly below this fractional boundary.

Example 2

Find the greatest integer satisfying the inequality.

Take the greatest integer strictly below this fractional boundary.

Your turn

Question 1

Find the greatest integer satisfying the inequality.

Check answer
Take the greatest integer strictly below this fractional boundary.
Question 2

Find the greatest integer satisfying the inequality.

Check answer
Take the greatest integer strictly below this fractional boundary.
Question 3

Find the greatest integer satisfying the inequality.

Check answer
Take the greatest integer strictly below this fractional boundary.
Question 4

Find the greatest integer satisfying the inequality.

Check answer
Take the greatest integer strictly below this fractional boundary.
Question 5

Find the greatest integer satisfying the inequality.

Check answer
Take the greatest integer strictly below this fractional boundary.
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