Inequalities practice
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.
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Expand grouped expressions and collect like terms before isolating the variable. Watch the sign of the final coefficient, then graph the exact boundary and direction.
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Each set has ten inequalities with exact integer boundaries. The number-line window follows the answer, so larger positive and negative solutions remain visible. The key repeats each problem and explains its equivalent transformations.
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
Simplify both sides and use equivalent transformations to describe a complete linear solution set.
Worked example
x ≤ −7.
Distribute to get 6x − 8 ≥ 8x + 6. Subtract 8x and add 8: −2x ≥ 14. Dividing by −2 reverses the comparison, giving x ≤ −7. The graph includes −7 and all smaller values.
Teaching notes
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Relationships select the literal operator printed in each prompt. Dividing by a negative coefficient reverses the normalized solution direction.
Combined operations adds like terms with constants and distribution with variables on both sides. Standard preserves the original worksheet mix.
A useful next step
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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Equations
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