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Graph inequalities on number lines or coordinate planes with proper notation
Graphing inequalities visually represents all solutions on a number line or coordinate plane. Understanding the notation and shading is key to correctly interpreting inequality graphs.
On a coordinate plane, vertical inequalities (x < a) create vertical boundary lines with left or right shading. Solid lines indicate inclusion (≤ or ≥), dashed lines indicate exclusion (< or >).
A closed (filled) circle means the endpoint is included in the solution (≤ or ≥), while an open (hollow) circle means it's not included (< or >).
Shade in the direction of the solutions. For x < 3, shade left (all numbers less than 3). For x > 3, shade right (all numbers greater than 3).
For AND (3 < x < 7), shade between two points. For OR (x < 2 OR x > 5), shade two separate regions.
A solid line means points on the line ARE included (≤ or ≥), while a dashed line means points on the line are NOT included (< or >).
Yes! For y inequalities (like y > 2), draw a horizontal line and shade above (for >) or below (for <). The same solid/dashed line rules apply.
Pick a point in the shaded region and substitute into the inequality. If it makes a true statement, your graph is correct. Also test a point outside the shaded region to verify it's false.
First solve the inequality to get x by itself (like x < 5), then graph the solution. Remember to flip the sign if you divide by a negative!
First convert to a compound inequality (|x| < 3 becomes -3 < x < 3), then graph the compound inequality with appropriate circles and shading.