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Identifying when two inequalities have no common solution

Identifying when two inequalities have no common solution.

  • 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 common solution, or explain why none exists.

This condition permits only values to the left of -5.This condition permits values starting at -3. Since -3 is greater than -5, the intervals do not overlap.

Example 2

Find the common solution, or explain why none exists.

This condition permits only values to the left of -4.This condition permits values starting at -2. Since -2 is greater than -4, the intervals do not overlap.

Your turn

Question 1

Find the common solution, or explain why none exists.

Check answer
This condition permits only values to the left of -3.This condition permits values starting at -1. Since -1 is greater than -3, the intervals do not overlap.
Question 2

Find the common solution, or explain why none exists.

Check answer
This condition permits only values to the left of -2.This condition permits values starting at 0. Since 0 is greater than -2, the intervals do not overlap.
Question 3

Find the common solution, or explain why none exists.

Check answer
This condition permits only values to the left of -1.This condition permits values starting at 1. Since 1 is greater than -1, the intervals do not overlap.
Question 4

Find the common solution, or explain why none exists.

Check answer
This condition permits only values to the left of 0.This condition permits values starting at 2. Since 2 is greater than 0, the intervals do not overlap.
Question 5

Find the common solution, or explain why none exists.

Check answer
This condition permits only values to the left of 1.This condition permits values starting at 3. Since 3 is greater than 1, the intervals do not overlap.
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