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Inequalities practice

One-step all-operations inequalities worksheets

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.

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Identify the operation on the variable, undo it on both sides, and graph the exact solution. Reverse the relationship only when the equivalent step multiplies or divides by a negative number.

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Keep the solution exact, then graph it

Each set has ten inequalities: three addition, three subtraction, two multiplication and two division questions. Every exact integer boundary stays visible on its number line, and the separate key explains each equivalent transformation.

The comparison checkboxes select symbols in the original question. A negative variable, a negative coefficient or the variable appearing on the right can mean that the solved inequality uses the opposite direction. Always normalize the relationship before choosing the ray.

Learning objective

What this activity builds

Choose the inverse operation, preserve or reverse the relationship correctly, and graph the exact solution set.

Worked example

Solve and graph 5 > x ÷ (−3).

x > −15.

Multiply both sides by −3 and reverse the relationship. Because the variable began on the right, the normalized answer is x > −15. Draw an open endpoint at −15 and a ray to the right.

Teaching notes

Make the practice count

  • Ask learners to name the inverse operation before calculating.
  • Compare the literal prompt relationship with the normalized answer.
  • Use the negative multiplication and division questions to discuss when reversal actually occurs.
  • Check a value below, at and above the boundary in the original prompt.

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Relationships select the literal operator printed in each prompt. Dividing by a negative coefficient reverses the normalized solution direction.

Every sheet has three addition, three subtraction, two multiplication and two division questions. The operation mix is fixed; choose any nonempty set of prompt relationships.

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Math SheetNameScore/ 10TeacherDateOne-Step All-Operations InequalitiesSolve each inequality. Show your work and graph the solution.1.r+43021222324252627282930312.n-2-13-16-15-14-13-12-11-10-9-8-7-63.9x996789101112131415164.n-3-613141516171819202122235.r+(-10)1419202122232425262728296.q-(-12)-3-20-19-18-17-16-15-14-13-12-11-107.-36-4z45678910111213148.-11y5-60-59-58-57-56-55-54-53-52-51-509.y+621101112131415161718192010.q-6-12-11-10-9-8-7-6-5-4-3-2-1math-sheet.comPage 1 / 1

A useful next step

Related activities

First page preview: Two-step inequalities worksheets

Inequalities

Two-step inequalities worksheets

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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