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 region satisfying the inequalities.
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.Test (0,0). This statement is true, so shade the side containing (0,0). Also require ≥ 0 and ≥ 0. Keep only the common region in the first quadrant.
Dashed boundaries exclude equality; solid boundaries include equality.
Example 2
Draw the region satisfying the inequalities.
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.Test (0,0). This statement is false, so shade the opposite side. Also require ≥ 0 and ≥ 0. Keep only the common region in the first quadrant.
Dashed boundaries exclude equality; solid boundaries include equality.
Your turn
Question 1
Draw the region satisfying the inequalities.
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.Test (0,0). This statement is true, so shade the side containing (0,0). Also require ≥ 0 and ≥ 0. Keep only the common region in the first quadrant.
Dashed boundaries exclude equality; solid boundaries include equality.
Question 2
Draw the region satisfying the inequalities.
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.Test (0,0). This statement is false, so shade the opposite side. Also require ≥ 0 and ≥ 0. Keep only the common region in the first quadrant.
Dashed boundaries exclude equality; solid boundaries include equality.
Question 3
Draw the region satisfying the inequalities.
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.Test (0,0). This statement is true, so shade the side containing (0,0). Also require ≥ 0 and ≥ 0. Keep only the common region in the first quadrant.
Dashed boundaries exclude equality; solid boundaries include equality.
Question 4
Draw the region satisfying the inequalities.
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.Test (0,0). This statement is false, so shade the opposite side. Also require ≥ 0 and ≥ 0. Keep only the common region in the first quadrant.
Dashed boundaries exclude equality; solid boundaries include equality.
Question 5
Draw the region satisfying the inequalities.
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.Test (0,0). This statement is true, so shade the side containing (0,0). Also require ≥ 0 and ≥ 0. Keep only the common region in the first quadrant.
Dashed boundaries exclude equality; solid boundaries include equality.
Draw the region satisfying the inequalities.
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.Test (0,0). This statement is true, so shade the side containing (0,0). Also require ≥ 0 and ≥ 0. Keep only the common region in the first quadrant.
Dashed boundaries exclude equality; solid boundaries include equality.
Draw the region satisfying the inequalities.
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.Test (0,0). This statement is false, so shade the opposite side. Also require ≥ 0 and ≥ 0. Keep only the common region in the first quadrant.
Dashed boundaries exclude equality; solid boundaries include equality.
Draw the region satisfying the inequalities.
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.Test (0,0). This statement is true, so shade the side containing (0,0). Also require ≥ 0 and ≥ 0. Keep only the common region in the first quadrant.
Dashed boundaries exclude equality; solid boundaries include equality.
Draw the region satisfying the inequalities.
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.Test (0,0). This statement is false, so shade the opposite side. Also require ≥ 0 and ≥ 0. Keep only the common region in the first quadrant.
Dashed boundaries exclude equality; solid boundaries include equality.
Draw the region satisfying the inequalities.
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.Test (0,0). This statement is true, so shade the side containing (0,0). Also require ≥ 0 and ≥ 0. Keep only the common region in the first quadrant.
Dashed boundaries exclude equality; solid boundaries include equality.