Valid Values Answer Key
About This Worksheet
This worksheet helps seventh-grade students decide which values satisfy a real-world inequality. Each problem includes a situation, an inequality, and a short set of possible values to test. Students circle every value that makes the inequality true, so they get practice thinking about solution sets rather than single answers. The contexts involve costs, points, weight limits, reading goals, event capacity, travel distance, and app spending. This makes the skill easier to understand because each solution has a real meaning.
What Students Practice
Students substitute candidate values into one-step and multi-step inequalities and determine whether the resulting statement is true or false. Some problems involve strict inequalities, while others include the boundary value with ≤ or ≥. This requires students to pay close attention to whether an exact limit is allowed. They also practice working with expressions that include fixed amounts and repeated costs. The result is a useful mix of substitution, arithmetic, and inequality reasoning.
Why This Matters
Students need to understand that an inequality usually has many possible solutions. Testing a set of values makes that idea visible because several choices may work while others do not. This also helps them understand why the boundary is included in some inequalities but excluded in others. That skill becomes important when students graph solution sets on number lines and solve more complicated algebraic inequalities. It also gives them a simple way to check whether their own solutions are reasonable.
Teaching Tips
Ask students to test one value at a time and write the result before deciding whether to circle it. Pay special attention to values that land exactly on the boundary, because those reveal whether the student understands the difference between < and ≤ or > and ≥. Encourage them to predict which values will work before calculating. Then have them explain why one value belongs in the solution set and another does not.
Curriculum Standards
This worksheet supports CCSS.MATH.CONTENT.7.EE.B.4.B by asking students to interpret and test solution sets for real-world inequalities. It also reinforces substitution and evaluation skills that students use throughout Grade 7 expressions and equations work. The activity is especially useful before or alongside graphing inequalities on a number line. It can serve as independent practice, homework, review, or a quick formative assessment.