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
Draw the boundary line only.
Replace the inequality sign with = to get the boundary line.Set to locate the -intercept .Set to locate . Draw a dashed line because equality is excluded.
Dashed boundaries exclude equality; solid boundaries include equality.
Example 2
Draw the boundary line only.
Replace the inequality sign with = to get the boundary line.Set to locate the -intercept .Set to locate . Draw a solid line because equality is included.
Dashed boundaries exclude equality; solid boundaries include equality.
Your turn
Question 1
Draw the boundary line only.
Check answer
Replace the inequality sign with = to get the boundary line.Set to locate the -intercept .Set to locate . Draw a dashed line because equality is excluded.
Dashed boundaries exclude equality; solid boundaries include equality.
Question 2
Draw the boundary line only.
Check answer
Replace the inequality sign with = to get the boundary line.Set to locate the -intercept .Set to locate . Draw a solid line because equality is included.
Dashed boundaries exclude equality; solid boundaries include equality.
Question 3
Draw the boundary line only.
Check answer
Replace the inequality sign with = to get the boundary line.Set to locate the -intercept .Set to locate . Draw a dashed line because equality is excluded.
Dashed boundaries exclude equality; solid boundaries include equality.
Question 4
Draw the boundary line only.
Check answer
Replace the inequality sign with = to get the boundary line.Set to locate the -intercept .Set to locate . Draw a solid line because equality is included.
Dashed boundaries exclude equality; solid boundaries include equality.
Question 5
Draw the boundary line only.
Check answer
Replace the inequality sign with = to get the boundary line.Set to locate the -intercept .Set to locate . Draw a dashed line because equality is excluded.
Dashed boundaries exclude equality; solid boundaries include equality.
Draw the boundary line only.
Answer
Replace the inequality sign with = to get the boundary line.Set to locate the -intercept .Set to locate . Draw a dashed line because equality is excluded.
Dashed boundaries exclude equality; solid boundaries include equality.
Draw the boundary line only.
Answer
Replace the inequality sign with = to get the boundary line.Set to locate the -intercept .Set to locate . Draw a solid line because equality is included.
Dashed boundaries exclude equality; solid boundaries include equality.
Draw the boundary line only.
Answer
Replace the inequality sign with = to get the boundary line.Set to locate the -intercept .Set to locate . Draw a dashed line because equality is excluded.
Dashed boundaries exclude equality; solid boundaries include equality.
Draw the boundary line only.
Answer
Replace the inequality sign with = to get the boundary line.Set to locate the -intercept .Set to locate . Draw a solid line because equality is included.
Dashed boundaries exclude equality; solid boundaries include equality.
Draw the boundary line only.
Answer
Replace the inequality sign with = to get the boundary line.Set to locate the -intercept .Set to locate . Draw a dashed line because equality is excluded.
Dashed boundaries exclude equality; solid boundaries include equality.