Solve, graph, and write linear inequalities from a described situation, including flipping the sign when multiplying/dividing by a negative.
Free, timed SHSAT practice sets on linear inequalities— every question includes a full worked explanation, and there's no account required.
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Solve an inequality like an equation, with one extra rule: when you multiply or divide both sides by a negative number, flip the sign.
Example: \(-2x + 10 \le 28\). Subtract \(10\): \(-2x \le 18\). Divide by \(-2\) and flip the sign: \(x \ge -9\). Adding or subtracting never flips the sign.
Words to symbols:
A weekly pay of \(40\) dollars plus \(6\) dollars a sale that must be at least \(130\) dollars is \(40 + 6s \ge 130\).
Whole-number answers: if \(s \ge 12.4\) and \(s\) counts sales, the least answer is \(13\). Round in the direction the sign points, then check the number in the original inequality.
Subtract 15: \(-4x ≥ 40\). Divide by -4 (negative), flipping the inequality: \(x ≤ -10\). (Forgetting to flip gives \(x ≥ -10\). Dividing by -4 first and then subtracting 15 gives \(x ≤ -115/4\). Dividing by 4 instead of -4 gives \(x ≥ 10\).)
The fixed \(50\) dollars plus \(5\) dollars per sale is the total, \(50 + 5s\). "At least \(100\)" means the total can equal \(100\) or be more, so the symbol is \(\ge\): \(50 + 5s \ge 100\). (\(\le\) points the wrong way: it means at most \(100\). \(>\) leaves out exactly \(100\). \(5 + 50s\) swaps the daily pay and the pay per sale.)
Write \(45 + 4s \ge 120\). Subtract \(45\): \(4s \ge 75\). Divide by \(4\): \(s \ge 18.75\). Sales are whole numbers, so round UP: \(19\). (\(18\) sales give only \(117\) dollars.)