Inequalities practice
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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Identify the two operations acting on the variable. Undo them on both sides in the appropriate order, reverse the comparison when needed, and graph the exact solution.
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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
Undo an added quantity and a coefficient or divisor in a sequence that preserves the solution set.
Worked example
x > −4.
Subtract 7 to get −3x < 12. Divide both sides by −3 and reverse the comparison: x > −4. The boundary is open, and the ray points right.
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.
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