Describe every value that makes an inequality true. Begin by graphing a comparison such as x < 4, or solve a two-step inequality before drawing its number-line solution.
A correct graph shows both the endpoint and the direction of all allowed values. Use the matching key after checking a few sample numbers in the original statement.
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For x > 4, draw an open circle at 4 and a ray to the right. The endpoint is excluded because 4 is not greater than 4. Values such as 5 and 4.5 satisfy the inequality; 3 does not. The ray represents infinitely many values, not only whole-number ticks.
Solve −2x + 3 < 11. Subtract 3 to get −2x < 8. Dividing both sides by −2 reverses the comparison, giving x > −4. Draw an open circle at −4 and shade to the right.
For that example, x = 0 gives 3 < 11, which is true. The value x = −5 gives 13 < 11, which is false. Testing a value on each side is a useful check on the direction of the ray.
Simple comparisons and number-line solution sets are a sixth-grade starting point. Solving two-step inequalities with signed coefficients is a seventh-grade extension. Adding or subtracting the same number does not reverse the sign; multiplying or dividing by a negative number does.