Inequalities practice
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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Undo multiplication or division on both sides. Reverse the inequality sign when multiplying or dividing by a negative number, then 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
Use a nonzero multiplier or divisor to isolate a variable and reverse order when that quantity is negative.
Worked example
x ≤ −12.
Multiply both sides by −4. Because the multiplier is negative, greater than or equal to becomes less than or equal to. Draw a filled endpoint at −12 and shade to the left.
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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