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Intersecting two solution intervals

Intersecting two solution intervals.

  • 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 values satisfying every inequality.

Both first conditions must hold, so take their overlap.Intersect with the final condition. Use the larger lower boundary and the smaller upper boundary.

Example 2

Find the values satisfying every inequality.

Both first conditions must hold, so take their overlap.Intersect with the final condition. Use the larger lower boundary and the smaller upper boundary.

Your turn

Question 1

Find the values satisfying every inequality.

Check answer
Both first conditions must hold, so take their overlap.Intersect with the final condition. Use the larger lower boundary and the smaller upper boundary.
Question 2

Find the values satisfying every inequality.

Check answer
Both first conditions must hold, so take their overlap.Intersect with the final condition. Use the larger lower boundary and the smaller upper boundary.
Question 3

Find the values satisfying every inequality.

Check answer
Both first conditions must hold, so take their overlap.Intersect with the final condition. Use the larger lower boundary and the smaller upper boundary.
Question 4

Find the values satisfying every inequality.

Check answer
Both first conditions must hold, so take their overlap.Intersect with the final condition. Use the larger lower boundary and the smaller upper boundary.
Question 5

Find the values satisfying every inequality.

Check answer
Both first conditions must hold, so take their overlap.Intersect with the final condition. Use the larger lower boundary and the smaller upper boundary.
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