A boundary, a direction, a set of solutions
Read a comparison, show every value that satisfies it, and explain each step. Begin with symbols and number-line rays, then solve with inverse operations, distribution and like terms.
Choose a worksheetDividing by a negative reverses order
Connect notation and meaning
Connect a comparison with its full set of solutions. Use the reference to discuss properties, then translate between notation and number-line rays.
Inequalities
Print a complete guide to inequality symbols, number-line graphs and equivalent transformations. Explore addition, subtraction, signed multiplication and division, and transitive comparisons with examples.
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Inequalities
Translate between an inequality and a number-line graph in twenty questions. Choose whole numbers, signed integers or halves; draw graphs, read graphs or mix both tasks, with a separate key.
Preview and downloadConnect notation and meaning
Start with addition and subtraction, then introduce signed multiplication and division. Use the combined sheet when learners are ready to choose among all four operations.
Inequalities
Solve and graph ten one-step inequalities using addition or subtraction. Practice expressions on either side, choose comparison symbols and print a worked solution key.
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Inequalities
Solve and graph ten one-step inequalities with signed coefficients and divisors. Learn when to reverse the comparison, using exact integer boundaries and explained answer keys.
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Inequalities
Solve and graph ten one-step inequalities in one mixed set: three addition, three subtraction, two multiplication and two division questions. Choose the prompt relationships and print separate worked answers.
Preview and downloadConnect notation and meaning
Combine inverse operations, distribution and like terms while keeping the same solution set. Every practice question ends with a number-line graph.
Inequalities
Solve and graph ten two-step inequalities with signed coefficients, constants and variable quotients. Keep boundaries exact and use the worked key to follow each equivalent transformation.
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Inequalities
Distribute factors, combine like terms and solve ten linear inequalities with variables on either or both sides. Print exact solutions, explained sign reversals and number-line graphs.
Preview and downloadCombine two conditions
AND keeps the intersection of two solution sets. OR takes their union. Solve chained or joined comparisons, then show the result with correct open or filled boundaries on a number line.
Inequalities
Solve and graph ten compound inequalities. Choose addition and subtraction, multiplication and division, or mixed operations, then connect AND intervals and OR rays with a separate graphical answer key.
Preview and downloadUse distance to describe a solution set
Isolate the absolute value before splitting the comparison. Practice shifts, adjustments outside the bars, negative inner coefficients and fractions, then graph an interval or two outward rays.
Inequalities
Solve and graph ten absolute value inequalities. Choose addition and subtraction, multiplication and division, or mixed operations, with shifts, negative inner coefficients and separate worked graphical answers.
Preview and downloadA familiar number domain helps learners focus on the comparison. Move to signed values and negative transformations when the endpoint and direction are secure.
Read the complete handout together, moving from open and filled endpoints to equivalent transformations.
Open this starting point →Draw twenty rays on a nonnegative number line, with positive variables and all four comparison symbols.
Open this starting point →Alternate ten graphing tasks with ten graph-reading tasks, including negative boundaries and half units.
Open this starting point →Compare positive and negative multipliers or divisors before moving to two-step inequalities.
Open this starting point →Mix three addition, three subtraction, two multiplication and two division questions in one ten-question review.
Open this starting point →Use additive and multiplicative inverse steps, then check the endpoint and ray in the original inequality.
Open this starting point →For x < 3, the value 3 is excluded but 2.9 is included. The graph describes all qualifying values, including values between labeled ticks. A worksheet with integer boundaries does not restrict the solution to integers.
Have learners test one value on each side and the boundary itself. This checks both the direction and whether equality is allowed.
An equation may ask for one value that makes two sides equal. A linear inequality usually describes a ray of possible values. Both use equivalent transformations, but multiplication or division by a negative number changes the direction of an inequality.
Adding or subtracting a negative number does not reverse the comparison. Write each operation explicitly to distinguish that step from division by a negative coefficient.
